Magnetism: Properties, Forces and Biot-Savart Law

Magnetism

• Electric force arises in two stages: a charge produces an electric field, than a second charge responds to it.
• Similarly, moving charge/current produces a magnetic field, and a second moving charge/current responds, producing magnetic force

Magnetic Field

• Magnetic fields can be represented by magnetic field lines
• Magnetic field lines are tangent to the magnetic field vector at a certain point
• Magnetic field lines never intersect
• Magnetic field lines are continuous loops
• Outside a magnet, the magnetic field lines point out of the North pole and into the South pole
• Inside a magnet, magnetic field lines are straight towards the north pole again
• The denser the magnetic field lines, the stronger the field
• The closer to the source, the stronger the field

Magnetic Poles

• Magnets are strongest at their poles
• Poles always exist in pairs with no such thing as a magnetic monopole
• If a magnet is broken, a new pole is generated and two magnets are yielded
• Unlike poles attract, like poles repel
• The further away from the pole something is, the weaker the magnetic field and force

Magnetization

• Magnetic properties can wear out over time or through demagnetization
• Demagnetization techniques include hammering, heating, or exposure to alternating currents, mixing up molecular arrangement and canceling polarity
• Demagnetized magnets can be magnetized again via exposure to another magnet with a strong magnetic field
• Magnetic forces between objects are due to interactions between moving electrons in atoms
• Inside a magnetized object, the motion of electrons are coordinated, an unmagnetized object has uncoordinated electrons

Magnetic Forces

• Magnetic force stems from the electromagnetic force, caused by the motion of charges
• Two objects containing charge moving in the same direction are attracted, while charges moving in opposite directions are repelled
• The induction of magnetic force is created with a moving charge/current creates a magnetic field and exerts force F on any other moving charge present
• A magnetic force on a moving charge has 4 characteristics It is proportional to the magnitude of the charge
• A magnetic force magnitude is proportional to the magnitude of the field
• A magnetic force is dependent on the particles velocity
• The magnetic force F is perpendicular to magnetic field B and velocity v
• Magnetic Force F = |q|vB = |q|vB sin Φ, where F is in N, q is magnitude of charge in C, and Φ is the angle betwen velocity v in m/s and magnetic field B in T
• Magnetic force can also be called Lorentz Force
• The right-hand rule can be used to determine the direction of the magnetic force, with the thumb being force Fm, the pointer being the current/charge v, and the middle finger being magnetic field B
• In a current-carrying conductor within a magnetic field, the conductor experiences a magnetic force F = ILB = IlB sin Φ, where F is in N, I is current in A, and Φ is the angle from segment of wire l in m to the direction of magnetic field B
• An alternative method, the palm can also determine mangetic force direction
• If the palm is direction of the force F, the thumb being current I and four fingers the direction of the magnetic field B

Right-Hand Grip Rule

• The rigth hand grip rule can determine direction of field an current.
• The thumb denots the direction of the current;
• The four remaining fingers denote direction of the magentic field

Nature of Magnetic Field

• The movement of charge within a magnetic field is circluar.
• The motion of a charged particle under the aciton of a magnetic field alone is always constant in speed.
• The radius of a particle R = mv / qB, where R is radius in m, m mass in kg, v is speed inv m/s, w is charge in C, and B is magnitude of magnetic field in T.
• If the charged particle is negative it moves clockwise around orbit.
• With initial velocity perpendicular to the magnetic field it experiance a force and right angle and will be steered into a ciruclar path.
• The number of revolutions per unit of time in magnetic field quantified by f = |q|B / 2Nm, where frequency is Hz, q is charge, B magnitude of magnetic field in T, and m mass

Magnetic Flux

• The magnetic flux throught a surface ФB is defined as the total number of magnetic field lines passsing through a gicen coil or area
  • ФB = BA = BA cos O
  • Where ФB is magnetic flux in Wb and A is area of surface in m
• If the surface coil is perpendicular to the magnetic field lines, flux is maximum and the angle 0 can be either 0 degree or 180
• If surface of coil is at certain angle to the magnetic field lines, flux is less than maximum but not zero
• If surface of coil is parallel, the flux is zero, angle is 90 dergeees

Biot-Savart's Law

• Determines magentic field at given point due to current
• Applied in problems with Asymmetrical elements
• dB = M0 * I dl sine o/ 4pi *r^2
• Where dB magentic field due to a point charge, Uo is magnetic constant 4pi x 10^-7, I current in A, dl is wire segment in m, r is distance from wire segment ot field, angle between a wire segement and an element of the charge
• For a infinitely long, straight wire
  • dB = Mo I /2Pi a
• For magnetic field at center of curcular current loop
  • dB = Mo NI / 2a

Ampere's Law

• For any closed loop, the dot product of the magnetic filed and the total distance around the loop = product of permiability copnstant and current enclosed by loop
• HIgh symmetry
• ∮dl=µ0I
• Given the summation of all the current-carrying elements around a circle, we get its circumference; and so the magnetic field generated by any point on a current is the same and constant
• dB = µ0I/2∏a
• For maagnetic feild for very long solenoid;
• dB = Mo N I/L

Electromagnetic Induction

• Magnetic flux through a soleoid causes a curent to to be induced, which is in turn caused by emelectromotive force

Experiements

• Stationary magnent is put near oe in a sole,oid. No current is induced
• A magnent moving either away or towards to a soleoid will generate some amount of energy
• Another soleoid that charge will current can indce emf in another soleoid; given one of them is in motion
• The induced emf is preoprtional to the rate of change of magentic flux

Faraday's Law

• The induced emf vaires proportionally to: # of turns in soleoid, diameter , change in angle between B and S, change in magnetic field, change in time
• e = -N d ØB/ dt
  • Where e is induced Emf in V, N is number of turns in soleoid, B is Magnetic feild in T, A is area in M^2, t Time in s
• Lenz's Law is also related to the principle of conservation of energy; if the induced current goes along with the changing flux, then the magnetic force on the object would accelerate it to a speed near infinity without any external energy source; this is a violation of energy conservation.
• The induced magnetic field always tries to keep the flux in a solenoid constant.

Electric Feild

• Electrostatic feilds start at positive charges and negativen charges.
• These are conservitive
• Indced electric feilds goto around in loops; not begin at a chargge
• They only requrie vanrying magnetic field. This ca n happen with our wihtout free electrons
• Theys are non conservitive

AC and DC Circuits

• AC is safer to transfer long distance, more power, 50-60Hz, reverses, varies with time, switch directions and got from generators
• DE is less power, shorter distance, no frequency, One direction, Constant,One direction, Cell or battery

Inductance

• Is disctivbe as the ratio of indcued voltuage opposed to the rate of change of crent causing it
• Indcutance is carried our by Indcutor, which is device
• Cuurrent increasse throught soleoid incrasiung magnetic field, a cahnge in magnetic feild will induced emf, then acts oppsoe what induces (Lenz)

Mutaul and Self

• Mutaul indcutacne is required other indcutor to indce back emf
• A cuirrent is flowiong coil 1 priduces B, and hence a magnetic Flux throught coil 2, Current in coll 1 change the flux, induicng ENF in coll 2
• Self inudtanc eis indstance that to opposes a flowign curuent or generates bakc ENF

Transformers

• Step up up down voltage
• For step down, the voltage is lower
• For step uup, th evultahe is highu

LC crcuits

• contain induuctor and a capicator
• charnge capiticor is connected to a inducer, th eenregy uscilallstes, call oscultary crcuit
• Potiential difference connected to iducer. A crrent willl increase the iducer and oppsoe ti
• The chrages are depletede at some point. Then induce ENF in the inducer and reverses its e ENF in that diuction,