XII Physics CH 13 Notes and Short Questions PDF

XII PHYSICS CH# 13 ELECTROMAGNETISM In the year 1819 Hans Christian Oersted, professor of physics during a lecture on simple cells connected to the wire observed that a magnetic needle placed near is deflecting.from this & later on many experiments he concluded tha...

XII PHYSICS CH# 13 ELECTROMAGNETISM In the year 1819 Hans Christian Oersted, professor of physics during a lecture on simple cells connected to the wire observed that a magnetic needle placed near is deflecting.from this & later on many experiments he concluded that a current carrying wire produces magnetic field. ELECTROMAGNETISM Branch of physics deals with the magnetic properties of current (moving charges) is called electromagnetism MAGNETISM Branch of physics deals with the properties of magnet is called magnetism MAGNETIC FIELD The space /region / volume around the magnet in which its effect can be observed is called magnetic field MAGNETIC FIELD OF A STRAIGHT CURRENT CARRYING WIRE Background In the year 1819 Hans Christian Oersted, professor of physics during a lecture on simple cells connected to the wire observed that a magnetic needle placed near is deflecting.from this & later on many experiments he concluded that a current carrying wire produces magnetic field. EXPERIMENT Let us consider a straight thick cupper wire passing vertically through a hole inside a card board. A thin layer of iron filling is then sprinkled on the card board. Now current is switched on and tape the card board gently. The iron filling set in a series of concentric circles about the wire as centre. a small compass placed on the card indicate the direction of the magnetic field lines. The direction of field lines are tangent to the circle.if the direction of current is reversed then the needle of compass is points opposite to the initial direction. The overall result of experiment is shown in the following diagram Prepared By: Waheed Ahmed 1 Lecturer in Physics (Research Scholar MS) XII PHYSICS Result Pattern of magnetic field In case of straight current carrying wire the magnetic field is in the form of concentric circles around the current carrying wire as centre Direction of magnetic field The direction of magnetic field can be determined by right hand rule that is If the wire is grasped in fist of right hand with the thumb pointing in the direction of the current, the fingers of the hand will circle the wire in the direction of magnetic field The direction of magnetic field depends upon the direction of current & magnetic field lasts as long as the current is flowing through the wire. FORCE ON A CURRENT CARRYING CONDUCTOR IN A UNIFORM MAGNETIC FIELD As we know that a current carrying wire produces magnetic field around itself. When this wire is placed inside external magnetic field it experience magnetic force. In order to find this magnetic force consider a current carrying wire placed at right angle to the external magnetic field as shown Prepared By: Waheed Ahmed 2 Lecturer in Physics (Research Scholar MS) XII PHYSICS MAGNITUDE OF FORCE The magnitude of force depends upon a) Orientation of the conductor Force is directly proportional to sin𝜃 that is F∝ sin𝜃 Equation 1 Where 𝜃 is the angle between conductor and the magnetic field  If conductor is parallel i:e 𝜃=0 then F=0  If conductor is perpendicular i:e 𝜃=900 then F=maximum b) Magnitude of current The force is directly proportional to the magnitude of current i:e F∝ I Equation 2 If we double the current the force will be doubled c) Length of the conductor The force is directly proportional to the length of the conductor i:e Prepared By: Waheed Ahmed 3 Lecturer in Physics (Research Scholar MS) XII PHYSICS F∝ I Equation 3 If length is doubled the force will be doubled d) Strength of the magnetic field 𝐵⃗ The force is directly proportional to the strength of the applied magnetic field i: e F∝B Equation 4 If we doubled the strength of magnetic field the force will be doubled Combining eq 1, 2, 3, & 4 we get F∝ ILBsin 𝜃 F =KILBsin𝜃 Where k is constant of proportionality, in SI system its value is one so above equation becomes F = ILBsin𝜃 Equation 5 In vector form ⃗ ×𝐵 F = I(𝐿 ⃗) Equation 6 This relation used for finding the force on a current carrying conductor placed inside the magnetic field.where 𝐿 ⃗ is in the direction of current flow. DEFINITION OF B If I=1A,L=1m and α= 900 then according to equation 1 ⃗ 𝐹 =𝐵 The force acting on one meter length of conductor placed at right angle to the magnetic field when a current of one ampere flow through it is called magnetic induction (magnetic flux density) ⃗ UNIT OF 𝐵 From equation 1 Prepared By: Waheed Ahmed 4 Lecturer in Physics (Research Scholar MS) XII PHYSICS 𝐹 B= 𝐼𝐿𝑠𝑖𝑛𝜃 𝑁 =𝐴𝑚 =N A-1 m-1=tesla ⃗ 𝑖𝑠𝑐𝑎𝑙𝑙𝑒𝑑𝑡𝑒𝑠𝑙𝑎denoted by T Hence the unit of 𝐵 ONE TESLA The magnitude of magnetic induction will be one tesla if one newton force acts on one meter current carrying conductor placed at right angle to the applied magnetic field when one ampere current flow through it. Another unit of magnetic induction is guass 1G=10-4T 1T=104G DIRECTION OF MAGNETIC FIELD Direction of magnetic force is determined by Fleming left hand rule as shown The thumb ,first finger and the second finger are set at right angled to each other with the first finger pointing in the direction of the magnetic field the second finger pointing in the direction of current the thumb gives the direction of force ALTERNATIVE METHOD TO DETERMINE THE DIRECTION OF FORCE (EXTENSION OF RIGHT HAND RULE) In order to find the direction of force consider the lines of forces as shown Prepared By: Waheed Ahmed 5 Lecturer in Physics (Research Scholar MS) XII PHYSICS The two fields tends to reinforce each other on the left hand side of the conductor & cancels each other on the right hand side of it.the conductor tends to move towards the weaker part of the field i:e the force on the conductor will be directed towards right in the direction of right angles to both the conductor and the magnetic field as shown above. RIGHT HAND PALM RULE If the middle finger of the right hand points in the direction of magnetic field, the thumb in the direction of magnetic current the force in the conductor will be normal to the palm towards the reader. MAGNETIC FLUX Definition The dot product of magnetic induction and vector area is called magnetic flux. SYMBOL Magnetic flux is denoted by φ Prepared By: Waheed Ahmed 6 Lecturer in Physics (Research Scholar MS) XII PHYSICS Diagram Mathematical form Let B is magnetic induction and A is area then magnetic flux φ is given as ⃗.𝐴 Φ = 𝐵 ⃗ |.|𝐴| cos 𝜃 Φ =|𝐵 Φ =BAcos 𝜃 Where 𝜃 is the angle between ⃗⃗⃗ 𝐵 and 𝐴 CASES OF MAGNETIC FLUX MAXIMUM The flux through area will be maximum if the surface is perpendicular to the field, because in this case normal to the surface will be parallel to magnetic induction as shown. Prepared By: Waheed Ahmed 7 Lecturer in Physics (Research Scholar MS) XII PHYSICS MINIMUM The magnetic flux through an area will be minimum if the surface is parallel to the field because in this case the normal to the surface will be perpendicular to the magnetic induction as shown. UNIT OF MAGNETIC FLUX SI magnetic flux is weber. One weber is given by 1Wb=1N m A-1 MAGNETIC FLUX DENSITY DEFINITION Magnetic flux per unit area is called magnetic flux density. SYMBOL It is denoted by B Prepared By: Waheed Ahmed 8 Lecturer in Physics (Research Scholar MS) XII PHYSICS MATHEMATICAL FORM Let φ is the magnetic flux and A is the area then magnetic flux density is given by φ B= 𝐴 UNIT OF MAGNETIC FLUX DENSITY SI unit of magnetic flux density if tesla and one tesla is given by 1T=1Wb m-2 AMPERE’S LAW circuits is called ampere’s law. STATEMENT The sum of quantities for all path elements into which the complete loop has been divided equals times the total current enclosed by the loop. MATHEMATICAL FORM Let us consider a current carrying straight wire as shown in figure Diagram If we consider a closed path around the wire in the form of circle having the wire at centre ,then the magnitude of magnetic flux density B changes with current I in the wire and the distance r from the wire Then B∝I Prepared By: Waheed Ahmed 9 Lecturer in Physics (Research Scholar MS) XII PHYSICS 1 & B∝ 𝑟 𝐼 Or B∝ 𝑟 Summing up all round the circle 𝐼 B=𝜇° 2𝜋𝑟 Where 𝜇° is the permeability of free space(4𝜋 ×10-7Wb A-1 m-1) B2𝜋r=𝜇° 𝐼 Now consider a closed path around the wire as shown for any path element ∆𝐿 we can write B.∆𝐿 = 𝜇° I Now sum over the entire close path, ∑ 𝐵. ∆𝐿=𝜇° 𝐼 This is the mathematical form of Ampere’s law. AMPERIAN LOOP The imaginary closed path around a current carrying assembly is called Amperian loop. APPLICATION Ampere’s law is an easy way to find the magnetic induction around a current carrying assembly for example Field due to current carrying solenoid SOLENOID A solenoid is a coil of an insulated copper wire wound on a circular cylinder with closed turns. Pattern of magnetic field of solenoid When current passes through it, magnetic field is produced with is uniform and strong inside the solenoid while outside it the field is negligibly weak. Direction of magnetic field Prepared By: Waheed Ahmed 10 Lecturer in Physics (Research Scholar MS) XII PHYSICS The direction of magnetic field due to solenoid depends upon direction of current. Magnitude of magnetic field strength due to solenoid Consider a solenoid through which the current I is passing in order to determine the magnetic field of induction B at any point inside the solenoid imagine a closed path “abcda” on the form of a rectangular. The rectangular is divided into four elements of length L 1, L2, L3, L4. L1 is along the axis inside the solenoid and L3 is far from the solenoid. By applying amperes circuital law B L1 + B. L2 + B. L3 + B. L4 = μo x current enclosed —– (I) Since B. L1 is parallel inside the solenoid B. L1 = BL1cos 0 = BL1 The field is very weak outside the solenoid is very weak and therefore it can be neglected thus B. L3 = 0 As B is perpendicular to L2 and L4 inside the solenoid therefore B. L2 = BL2cos 90 = 0 B. L4 = BL4cos 90 = 0 substitute the above values is eq (I) B. L1 + O + 0 + 0 = μo x current closed B. L1 = μo x current enclosed ——- (II) If there are n turns per unit length of the solenoid and each turn carries a current I then the current in L1 segment will be nI L1then above equation will become B=μonI This is the strength of the magnetic field inside the solenoid. Dependence of magnetic field strength due to solenoid 1. Magnitude of current 2. Number of turns per unit length 3. Nature of medium as core APPLICATIONS OF MAGNETIC FIELD The strength of electromagnet depends upon 1) Number of turns around the magnetic core Prepared By: Waheed Ahmed 11 Lecturer in Physics (Research Scholar MS) XII PHYSICS 2) Magnitude of current through the wire 3) Size of the iron core By increasing these factors we can construct a powerful magnet than natural magnet which can be used to lift heavy loads (steel objects). In industrial magnet soft iron core is used whose magnetism can be removed just by cutting of the supply of current.some of the applications of such type of electromagnets are as under Cranes Strong electromagnets are often used in cranes to move large pieces of iron or steel. Electromagnetic locks There are two types of electromagnetic locks used in doors a. An electromagnetic lock is used to lock a door by creating a strong magnet field in an electromagnet that is in contact with a magnetic plate. As long as there is current through the electromagnet, the door remains closed and locked. b. Another type of electromagnetic lock electromagnet to extend a plunger between the door making it nearly impossible to open the door until the electromagnet releases the plunger. Prepared By: Waheed Ahmed 12 Lecturer in Physics (Research Scholar MS) XII PHYSICS Doorbell ringe FORCE ON A CHARGE MOVING IN UNIFORM MAGNETIC FIELD When a charged particles moves across a magnetic field, a magnetic force is experienced by the charged particle. The magnitude of force on the charge depends on the following factors:  Magnetic force is directly proportional to the magnitude of charge. F∝ q  Magnetic force is directly proportional to the velocity of the charged particle. F∝V  Magnetic force is directly proportional to the intensity of magnetic field or magnetic flux density. F∝B  Magnetic force is directly proportional to the sin𝜃 F∝Sin𝜃 Combining above statements: F∝qVBSin𝜃 OR Prepared By: Waheed Ahmed 13 Lecturer in Physics (Research Scholar MS) XII PHYSICS F=KqvBsin𝜃 Here the value of constant k is unity i.e. K= 1 Then above equation will be F=qvBsin𝜃 The direction of force will be perpendicular to the plane formed by B and V. DETERMINATION OF e/m OF AN ELECTRON Background J.J Thomson was the first scientist who measured charge to mass ratio (e/m) of an electron. Importance e/m is measured to find the mass of electron because charge is known by Millikan oil drop experiment Diagram Prepared By: Waheed Ahmed 14 Lecturer in Physics (Research Scholar MS) XII PHYSICS Derivation When a narrow beam of charged particles are projected at constant speed (v) across a magnetic field in a direction perpendicular to the field, the beam of particles experiences a force, which makes them move in a circular path.Then 𝑚𝑣 2 = 𝑒𝑉𝐵 𝑟 𝑒 𝑣 = 𝑚 𝐵𝑟 Where B=magnetic field strength r=radius of electron since KE of electron is due to the electrical energy supplied to it so 1 𝑚𝑣 2 = 𝑒𝑉 2 𝑚𝑣 2 = 2𝑒𝑉 2𝑒𝑉 𝑣2 = 𝑚 𝒗𝟐 = 2𝑒𝑉 𝑣=√ 𝑚 Putting in above equation we get 2𝑒𝑉 𝑒 √𝑚 = 𝑚 𝐵𝑟 Prepared By: Waheed Ahmed 15 Lecturer in Physics (Research Scholar MS) XII PHYSICS Squaring on both sides 2𝑒𝑉 𝑒2 2 = 2𝑚 2 𝑚 𝐵 𝑟 𝑒 2 𝑒 2𝑉 ( ) =( ) 2 2 𝑚 𝑚 𝐵 𝑟 𝑒 2𝑉 = 2 2 𝑚 𝐵 𝑟 This is the formula used to find the e/m of electron.where 𝑉 = 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑘𝑛𝑜𝑤𝑛 𝐵 = 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑓𝑖𝑒𝑙𝑑 𝑐𝑎𝑛 𝑏𝑒 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑢𝑠𝑖𝑛𝑔 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑟 = 𝑟𝑎𝑑𝑖𝑢𝑠 𝑖𝑠 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑑 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡 𝑚𝑎𝑘𝑖𝑛𝑔 𝑡ℎ𝑒 𝑝𝑎𝑡ℎ 𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏𝑦 𝑢𝑠𝑖𝑛𝑔 a gas like hydrogen or He inside the tube. NUMERICAL VALUE OF e/m After substituting the values we get e/m = 1.75888x1011 C/Kg VELOCITY SELECTOR Definition An arrangement of cross electric & magnetic field used to gain a charge from beam moving at specific velocity or to pass a charge straight is called velocity selector BASIC PRINCIPLE Magnetic force acting on charge particle is balanced by the electrical force on it. MATHEMATICAL FORM Let a charge q moves with velocity v inside a constant magnetic field B then magnetic force acting on charge particle Fm is given by Fm= qvB If there is cross electric field in this region as shown in below fig then this electrical force is given by Prepared By: Waheed Ahmed 16 Lecturer in Physics (Research Scholar MS) XII PHYSICS Fe = qE Comparing above two equationswe get qvB=qE vB=E 𝐸 v=𝐵 This is the working equation of velocity selector Prepared By: Waheed Ahmed 17 Lecturer in Physics (Research Scholar MS) XII PHYSICS USES To get a charge of desired velocity from a beam of particles To find the velocity of charge particles TORQUE ON A CURRENT CARRYING COIL Consider a rectangular coil of wire through which an electric current 'I' is being passed. The coil is placed in a uniform magnetic field of magnitude "B". The vertical side AB of the coil experiences a force F which is directed perpendicular into the paper. There is an equal and opposite force F on side CD. Since the plane of coil is parallel to the magnetic field therefore there is no force on either side AC and BD. Force on AB and CD will produce torque in these arms. In this case L perpendicular to B i.e. 𝜃 = 90, hence F = BIL (1) F = BIL τAB = b/2 (BIL)…………(1) Similarly τCD = b/2 (BIL)…………(2) These two torque result in a couple in the coil and the coil starts moving (rotating) in magnetic field. Since both the torque are trying to rotate the coil in the same direction, therefore the total torque produced in the coil will be the sum of all the individuals torque. τ = τ𝑨𝑩 + τ𝑪𝑫 τ = b/2 (BIL) + b/2 (BIL) τ= 2/2 b (BIL) τ= IB (Lb) but Lb = area of coil = A Prepared By: Waheed Ahmed 18 Lecturer in Physics (Research Scholar MS) XII PHYSICS τ= IBA If there are "N" number of turns of wire in the coil then the torque will becomes N times τ= BINA When the coil makes an angle a with the direction of magnetic field, the torque will become τ= BINA Cos𝜽 MAGNETIC RESONANCE IMAGING (MRI) DEFINITION Most advance diagnostic tool used a combination of a strong magnetic field and radio waves to produce a high resolution image of inside of the body is called magnetic resonance imaging BASIC PRINCIPLE Protons interact with strong magnetic field and radio waves to generate electrical pulses that can be digitally processed CONSTRUCTION MRI generally consist of following components a. MAIN MAGNET used for producing strong magnetic field b. RADIOFREQUENCY SYSTEM consist of radiofrequency transmitter which provides energetic rays to specimen and radiofrequency receiver which collect the radiated waves from the specimen c. GRADIENT COIL consist of three orthogonal coils produces gradient magnetic field along each axis d. COMPUTER collect the information from RF coils and solve hundred thousand equations to produce high resolution image Prepared By: Waheed Ahmed 19 Lecturer in Physics (Research Scholar MS) XII PHYSICS WORKING & THEORY Human body is composed primarily of fat and water; it is made up of mostly of hydrogen atoms. When human body is placed into MRI then the following steps occur. 1. The strong magnetic field aligns the hydrogen protons in its direction and these willprecess with specific frequency. 2. Now RF waves of specific frequency are made incident upon the body. The protons absorb these radiations by the phenomena of resonance, after relaxation time these protons will emit energy waves. 3. The emitted energy waves (signal) then picked by the RF coil and then transmitted to the computer. 4. Computer process this data & provides an image. USES a. MRI is widely used to study brain function. b. MRI is capable of imaging movement of the walls of heart and injection of fluid into the blood. c. MRI is able to create detailed image to assist the diagnosis of cancer & heart deases ADVANTAGE Prepared By: Waheed Ahmed 20 Lecturer in Physics (Research Scholar MS) XII PHYSICS It is a non-invasive technique for imaging soft tissue in the body. DISADVANTAGE a. It is an expensive tool for diagnosis. b. It cannot be operated on artificial heart valves,joint metal pins other metal object containing bodies. GALVANOMETER DEFINITION An electrical instrument used to detect the passage of electric current is called galvanometer. BASIC PRINCIPAL A current carrying loop placed in a magnetic field experiences a torque. CONSTRUCTION Galvanometer consists of 1) U shaped magnet for producing intense and radial field. 2) Rectangular coil consist of N numbers of turns. 3) Soft iron core. Soft iron a cylindrical shape around which the rectangular coil is wounded to increase the strength of magnetic field and to avoid damage to the coil. Prepared By: Waheed Ahmed 21 Lecturer in Physics (Research Scholar MS) XII PHYSICS WORKING AND THEORY When a current I flows through the coil, a magnetic field is set up which interacts with that of permanent magnet B producing a torque 𝜏 is given by 𝜏=NIABcos𝜃 Where N=number of turns in the coil A=area of the coil B= magnetic induction of the radial magnetic field 𝜃 =angle between the plane of the coil and the direction of B Since magnetic field is radial, the plane of the coil is parallel to the magnetic field B, so 𝜏 = 𝑁𝐵𝐼𝐴 The torque rotates the coil and twist the suspension ribbon,until it is fully resisted by the suspension. As a result a restoring torque comes into play trying to restore the coil back to original position. If 𝜃 be the twist produced in the strip and C is the restoring torque per unit twists then; Restoring torque = 𝜏 = 𝐶𝜃 When the coil is in equilibrium then the deflecting torque is equal to the restoring torque then Prepared By: Waheed Ahmed 22 Lecturer in Physics (Research Scholar MS) XII PHYSICS NIAB=𝐶𝜃 𝐶𝜃 I=𝑁𝐴𝐵 Where C/NAB is a constant then I∝ 𝜃 So current is proportional to the angular displacement.if we measure the angular displacement we measure the current on the scale. SENSITIVITY OF GALVANOMETER A galvanometer is more sensitive if it make large deflection for small current and this is achieved by making C/NBA small. CALIBRATION METHOD There are two methods commonly used for observing the angle of deflection of the coil 1) Lamp scale method. In sensitive galvanometer this arrangement is used in this arrangement small mirror is attached with coil along with lamp and scale. A beam of light from the lamp is directed towards the mirror of the galvanometer. After reflection from the mirror it produces us spot on a translucent scale placed at a distance of one meter from the galvanometer. As the coil along with the mirror rotates the spot of light moves along the scale. The displacement of the spot of light on the scale is proportional to the angle of deflection (provided the angle of deflection is small). 2) Pivoted Coil Galvanometer In less sensitive galvanometer the coil is pivoted between two jeweled bearings the restoring torque is provided by two hairs springs which also serves as current lead. A light aluminum pointer is attached to the coil which moves over the scale thus giving the angle of deflection of coil. AMMETER Ammeter is an electrical measuring device, which is used to measure electric current through the circuit. It is the modified form of galvanometer CONNECTION OF AMMETER IN CIRCUIT Prepared By: Waheed Ahmed 23 Lecturer in Physics (Research Scholar MS) XII PHYSICS An ammeter is always connected in series to a circuit. SYMBOL CONVERSION OF GALVANOMETER INTO AMMETER Since Galvanometer is a very sensitive instrument therefore it can’t measure heavy currents. In order to convert a Galvanometer into an Ammeter, a very low resistance known as "shunt" resistance is connected in parallel to Galvanometer. Value of shunt is so adjusted that most of the current passes through the shunt. In this way a Galvanometer is converted into Ammeter and can measure heavy currents without fully deflected. VALUE OF SHUNT RESISTANCE Let resistance of galvanometer = Rg and it gives full-scale deflection when current Ig is passed through it. Then, Vg = IgRg -------(i) Let a shunt of resistance (Rs) is connected in parallel to galvanometer. If total current through the circuit is I. Then current through shunt: Is = (I-Ig) potential difference across the shunt: Vs= IsRs or Vs = (I – Ig)Rs -------(ii) But Vs =Vg (I - Ig)Rs = IgRg VOLT METER Prepared By: Waheed Ahmed 24 Lecturer in Physics (Research Scholar MS) XII PHYSICS Voltmeter is an electrical measuring device, which is used to measure potential difference between two points in a circuit. CONNECTION OF VOLTMETER IN CIRCUIT Voltmeter is always connected in parallel to a circuit. SYMBOL CONVERSION OF GALVANOMETER INTO VOLTMETER Since Galvanometer is a very sensitive instrument, therefore it can not measure high potential difference. In order to convert a Galvanometer into voltmeter, a very high resistance known as "series resistance" is connected in series with the galvanometer. VALUE OF SERIES RESISTANCE Let resistance of galvanometer = Rg and resistance Rx (high) is connected in series to it. Then combined resistance = (Rg + Rx). If potential between the points to be measured = V and if galvanometer gives full-scale deflection, when current "Ig" passes through it. Then, V = Ig (Rg + Rx) V = IgRg + IgRx V – IgRg = IgRx Rx = (V – IgRg)/Ig Thus Rx can be found. AVOMETER- MULTIMETER Definition An instrument used to measure current, voltage and resistance is called AVO meter or multimeter It is combination of ampere meter, voltmeter and ohmmeter so it is called as AVO meter Construction Prepared By: Waheed Ahmed 25 Lecturer in Physics (Research Scholar MS) XII PHYSICS it consist of galvanometer with combination of resistors all enclosed in a box. it has different scales graduated in such a manner that all the three quantities can be measured. it has its own battery for its function and for operating the electrical circuits. The quantity to be measured and range is selected by a selector switch which connect the particular circuit to the galvanometer as shown Current measurement For current measurement the selector switch is turned to X2.this circuit is a series combination of shunt resistance called universal shunt as shown Any one of this shunt can be used for the measurement of current in different ranges. This provides a safe method of switching between current ranges without any danger of excessive current through the meter. Voltage measurement For measuring voltage the voltage selector switch of the AVO meter changes the circuit to as shown This circuit allows selecting any range and corresponding highresistance to be connected in series with the galvanometer. The added high resistance converts the galvanometer to a voltmeter of specific range. Resistance measurement For resistance measurement the selector switch uses the circuit as shown Prepared By: Waheed Ahmed 26 Lecturer in Physics (Research Scholar MS) XII PHYSICS The leads are connected across the resistance to be measured. The battery of the meter supplies current to the meter for deflection which in turn varies with the external resistance and can be calibrated the amount of deflection on the ohms scale indicates directly the magnitude of resistance. The ohmmeter reads up the scale regardless of the polarity of the leads because the polarity of the internal battery determines the direction of the current through the galvanometer. DIGITAL MULTIMETER Modern multimeter are often digital due to their accuracy,durability and extra features. In a digital multimeter the signal under test is converted to a voltage and an amplifier with electronically controlled gain preconditions the signal. A digital multimeter displays the quantity measured as a number which eliminates the parallax error. CONCEPTUAL QUESTIONS Q#1 what is the force that a conductor of length L carrying a current I, experience when placed in a magnetic field B? What is the direction of this force? Answer: when a conductor of length L carrying current I is placed in the magnetic field B then the magnitude of force acting on the conductor will be F=ILBsinα In vector form ⃗ ×𝐵 F=I (𝐿 ⃗) a. If L &B are parallel then F=0 b. If L & B are perpendicular then F=ILB Prepared By: Waheed Ahmed 27 Lecturer in Physics (Research Scholar MS) XII PHYSICS Direction of the force Direction of force is determined by Fleming left hand rule that is The thumb ,first finger and the second finger are set at right angled to each other with the first finger pointing in the direction of the magnetic field the second finger pointing in the direction of current the thumb gives the direction of force Alternative method (extension of right hand rule) In order to find the direction of the force, consider the lines of forces as shown The two fields tend to reinforce each other on the left hand side of the conductor and cancel each other on the right hand side of it. The conductor tends to move towards the weaker part ot the field that is the force on the conductor will be directed towards right in a direction at right angle to both the conductor and the magnetic field. Q#2 what is the nature of force between two parallel current carrying wires (in the same direction)? Answer: The force between two parallel current carrying wires having in same direction will be attractive as shown by the figure According to the pattern of the magnetic field around the wires as shown in above figure They cancels each other between themselves and at the outer part they remains same so the conductor will move from the denser part of the field to the weaker part of the field. as a result both wires movies towards each other that means attractive force exist between the wires. Prepared By: Waheed Ahmed 28 Lecturer in Physics (Research Scholar MS) XII PHYSICS Q#3 what is the magnitude of the force on a charge q moving with a velocity v in a magnetic field? Answer: when charge particle q movies inside the magnetic field of strength B with velocity v then the force acting on charge will be ⃗) 𝐹 =q (𝑣 × 𝐵 In magnitude form F=qvBsinα This is the magnitude of force on the charge particle inside the magnetic field. a. If charge q enters inside magnetic field parallel then the force exerted will be zero that is Fm =0 because 𝜃 =0 & sin𝜃 =0 b. If charge enters inside the magnetic field perpendicular then the force exerted will be maximum that is F=qvB because 𝜃 =900 & sin𝜃=1 Q#4 in a uniform magnetic field B an electron enters with velocity v write the expression for the force experienced by electrons. Answer: the force on an electron moving inside the uniform magnetic field B is ⃗ ) = −𝑒(𝑣 × 𝐵 𝐹𝑚 = −𝑞(𝑣 × 𝐵 ⃗) That can be proved as The magnitude of force on the charge depends on the following factors:  Magnetic force is directly proportional to the magnitude of charge. F∝q  Magnetic force is directly proportional to the velocity of the charged particle. F∝V  Magnetic force is directly proportional to the intensity of magnetic field or magnetic flux density. F∝B Prepared By: Waheed Ahmed 29 Lecturer in Physics (Research Scholar MS) XII PHYSICS  Magnetic force is directly proportional to the sin𝜃 F∝Sin𝜃 Combining above statements: F∝qVBSin𝜃 OR F=KqvBsin𝜃 Here the value of constant k is unity i.e. K= 1 Then above equation will be F=qvBsin𝜃 In vector form it can written as ⃗) 𝐹𝑚 = 𝑞(𝑣 × 𝐵 But charge of electron is negative and is denoted by e so ⃗ ) = −𝑒(𝑣 × 𝐵 𝐹𝑚 = −𝑞(𝑣 × 𝐵 ⃗) The direction of force will be perpendicular to the plane formed by B and V & is determined by right hand rule. Q#5what will be the path of a charged particle moving in a uniform magnetic field at any arbitrary angle with the field? Answer: when a charge particle enters into magnetic field at any arbitrary angle it will follow the path of circle and at the end of half of the circle it will left out the magnetic field as shown Q#6 an electron does not suffer any deflection while passing through a region. Are you sure that there is no magnetic field? Prepared By: Waheed Ahmed 30 Lecturer in Physics (Research Scholar MS) XII PHYSICS Answer: no we cannot conclude about the presence of magnetic field if an electron does not deflect a region because it can be parallel to the magnetic field line as F=qvBsin𝜃 If 𝜃=0 then F=0 with q≠0,v≠0&B≠ 0 so we can say that electron is parallel to the magnetic field will not deflect.thus a straight moving electron does not implies that there is no any magnetic field. Q#7 an electron beam passes through a region of crossed electric and magnetic fields of intensity E and B respectively. For what value of the electron speed the beam will remain un-deflected? Answer: if the speed of electron is equal to the ratio of electric field strength to the magnetic field strength then electron will pass un-deflected through cross electric and magnetic field Proof: Let a charge q moves with velocity v inside a constant magnetic field B then magnetic force acting on charge particle Fm is given by Fm= qvB If there is cross electric field in this region as shown in below fig then this electrical force is given by Fe = qE Comparing above two equations we get qvB=qE vB=E 𝐸 v=𝐵 This is the working equation of velocity selector Q#8 uniform electric and magnetic fields are produced pointing in the same direction. An electron is projected in the direction of the fields. What will be the effect on the KE of the electron due to two fields? Prepared By: Waheed Ahmed 31 Lecturer in Physics (Research Scholar MS) XII PHYSICS Answer: when an electron is projected in magnetic field and electric field pointing in same direction parallel to the field lines then its kinetic energy will change due to the electric field but remains same due to magnetic field Effect of magnetic field: when electron is projected parallel to the magnetic field then the force exerted by the magnetic field is zero as Fm=qvBsin𝜃 Since 𝜃=0 This implies that Fm=0 So there will be no there will be no change in the kinetic energy of electron according to work energy principle Effect of electric field : when an electron is projected along the electric field then the electrical force will oppose the motion of electron according to equation F=-qE So the speed of electron decreases as a result the kinetic energy of electron will decrease. Q#9what is the cyclotron frequency of a charge particle of mass m,charge q moving in a magnetic field B? Answer:when a charge particle q of mass m movies inside the uniform magnetic field of strength B it will follow the circular path and the maximum magnetic force acting on charge particle will be Fm=qvB This force plays the role of centripetal force so Fc=mv2/r=m𝜔2/r Equating equation 1 and equation 2 we get m𝜔2r=qvB m(𝜔𝑟)𝜔=qvB but𝜔𝑟 = 𝑣 so m𝜔𝑣 = 𝑞𝑣𝐵 m𝜔 = 𝑞𝐵 Prepared By: Waheed Ahmed 32 Lecturer in Physics (Research Scholar MS) XII PHYSICS but𝜔 = 2𝜋𝑓 so 2m𝜋𝑓 = 𝑞𝐵 𝑞𝐵 f=2𝜋𝑚 This is the frequency of cyclotron. From this relation it is clear that this is independent of speed of charge particle. Q#10Can neutron be accelerated in a cyclotron? Give reason. Answer: no because neutrons are electrically neutral and cyclotron is used to accelerate the charge particle.the cyclotrons frequency is given by 𝑞𝐵 f=2𝜋𝑚 Since neutron is neutral so q=0 f=0 So neutron will not move in circular path so cannot be accelerated by cyclotron Q#11.A current carringloop,free to turn,is placed in a uniform magnetic field B.What will be its orientation relative to B,in the equilibrium state.? Answer: when plane of the coil placed inside the magnetic field is perpendicular to the magnetic lines of forces then it will be in state of equilibrium. Proof Since torque acting on the current carrying coil place inside the magnetic field is given by 𝜏 = 𝑁𝐼𝐵𝐴 cos 𝜃 Where N= number of turns of the loop A=area of the loop I=current through the loop B=magnetic flux density 𝜃 = Angle between the plane of the coil and magnetic field So if angle between the plane of the coil and magnetic field is 90 0then cos90 is zero that is 𝜏=0 This is the condition of equilibrium. So for a current carrying coil free to rotate placed inside the magnetic field is in equilibrium if its plane of coil is perpendicular to the field. Prepared By: Waheed Ahmed 33 Lecturer in Physics (Research Scholar MS) XII PHYSICS Q#12How does a current carrying coil behave like a bar magnet? Answer: a current carrying coil behaves as a bar magnet because one face of the coil behave as north pole and other behave as south pole. The magnetic field produced by the current carrying coil is similar to the magnetic field of bar magnet as shown Prepared By: Waheed Ahmed 34 Lecturer in Physics (Research Scholar MS)