Electrostatics: Charges and Coulomb's Law

• A static electric charge creates only an electric field.
• When charge is placed on a good conductor, it remains on the surface.
• 6.25 x 10^18 electrons have a charge equal to 1 Coulomb.
• A neutral body can be positively charged by removing electrons from its surface.
• The Coulomb is the SI unit of electric charge.
• Coulombian force may be attractive or repulsive.
• Rubbing two appropriate bodies together results in the production of a positive charge.
• If one electron is removed from 0.01% of atoms in a 1g object containing 5 x 10^21 atoms, the charge on the sphere will be +0.08.
• Giving a soap bubble positive charge will increase its radius.
• An electroscope is used find the presence of charge on a substance .
• There will be repulsion between two like charges and attraction between two unlike charges.
• In the formula F = k * q1 * q2 / r^n representing Coulomb's law, n = 2.
• Coulomb's law is correct for distances greater than 10^-15 m and less than 10^18 m.
• The flux associated with any point in an electric field is zero.
• The unit and dimensional formula of volume charge density is Cm^-3, [M^0 L^-3 T^1 A^1].
• Alpha particles are deflected in an electric field.
• The unit of dipole moment is Cm.
• If the force acting on a 6.4 × 10^-3 C point charge in a uniform electric field is 0.128N, the electric field at the point is 20 N/C.
• To keep a water drop of radius 10^-5 cm suspended in air when charged with one electron, the required electric field intensity is approximately 130 N/C.
• The unit of electric field intensity is N/C.
• The SI unit of electric flux is Vm.
• If a 10 × 10^-6 C charge is uniformly spread over a cube with a face length of 1 mm, the charge density will be 10^4 Cm^-3.
• Flux associated with a metal piece of 1 m^2 cross-section placed in an electric field of 2i N/C is 2.
• When an electric dipole is placed at the centre of a sphere, the flux passing through the surface of the sphere cannot be found.
• When the electric flux linked with the surface will be positive when 0 < 90°.
• For a charged sphere, if σ and ρ are surface and volume charge densities, then ρ = 0, σ ≠ 0.
• Fleming's right hand rule describes the direction of induced current in a moving conductor within a magnetic field.
• Faraday's law on electromagnetic induction gives the value of induced emf.

Square Loop in Magnetic Field

• When a square loop of length L and resistance R is moved with velocity v in a uniform magnetic field B, no current is induced.

DC Motor

• A D.C. motor working on 200V with an initial current of 5A attains maximum velocity at 3A, its Back emf will be 80 V.

Electromagnetic Force

• For 5 × 10^-4 field lines passing through a 1000 turn coil in a time interval to produce an electromotive force of 5V, the time interval will be 0.01 s.
• When a bar magnet moves with velocity v towards coil (2), the south pole is induced on the face of coil (1) towards the magnet.
• If the refractive index of glass with respect to air is 1.8, the refractive index of air with respect to glass is 0.556.
• If two ions of charge +q are at distance d and force between them is F, then the number of electrons removed from each is √(Fd^2/ke^2).
• Given E = (3/5)i + (4/5)j, the electric flux through an area of 0.4 m^2 parallel to the y-z plane is 0.24 Nm^2/C.
• An electric dipole at 30° with a 2 × 10^5 N/C uniform electric field experiences a torque of 4 Nm; the charge at one end of the dipole is 2 mC if the dipole length is 2 cm.
• The electric potential is found to be 5 V throughout a region of space with volume 0.2 m³, the magnitude of electric field in this region is zero.
• Two point-like charges of +16µC and -9µC are 10cm apart in air, the resultant electric field will be zero at a distance of 30 cm from -9µC charge.
• The dimensional formula of electric field intensity is [M¹L¹T^-3A^-1].
• Two point electric charges of +10^-8 C and -10^-8 C are placed 0.1 m apart; at the centre of the line joining them the magnitude of total electric field is 7.2 × 10^4 NC^-1.
• An infinite line charge produces a field of 9 x 10^4 NC^-1 at 2 cm; the produced electrical field at 3 cm is 6 × 10^4 NC^-1.
• The charge equivalent to 6 × 10^18 electrons is -1 C.
• If a body contains n₁ protons and n₂ electrons, the total charge on the body is (n₁ - n₂)e.
• Electric field due to a uniformly charged infinite plane sheet does not depend on r.
• When a proton moves opposite an electric field, the work done on it by the electric field is negative, and the electrostatic potential energy of the proton increases.

Charged Sphere

• For a charged sphere of radius R charged up to potential V, the electric field at distance r (where r > R) from the sphere's centre is VR^2 / r^2.
• If a positive charge is brought to a higher potential from a lower potential, then its potential energy increases.
• For 10 capacitors each of 10µF, the ratio of maximum to minimum capacitance obtained by their combination is 100:1.
• A spherical capacitor of 1µF has a diameter of 1.8 × 10^4 m.
• For 4 µF and 6 µF capacitors joined in series with 500 V applied, the charge on each plate is 1.2 × 10^-3 C.
• A capacitor having a capacitance of 600 µF is charged uniformly at a rate of 50 µC/s, it will take 120 s to increase its potential by 10 volts.
• Considering the Earth to be a metallic sphere, its capacitance would be nearly 700 μF (using R = 6400 km, ε₀ = 8.85 × 10^-12 SI unit).
• In a parallel plate capacitor filled with a medium of dielectric constant K, the electric field becomes 1/K times and the capacitance becomes K times.
• A capacitor works with both AC and DC supply.
• If a sphere has potential V, electric field F at its surface, and surface charge density σ, doubling its radius without changing σ will alter the ratio of new potential to initial electric field as R:1.
• A spherical conductor of radius 12 cm with a charge of 1.6 × 10⁻⁷ C distributed uniformly on its surface has an electric field of 10⁵ NC⁻¹ just outside the sphere.
• Three capacitors each of capacitance 9 pF connected in series have a total capacitance of 3 pF.
• The capacitance of a parallel plate capacitor with air between the plates, each plate having an area of 6 × 10⁻³ m² and a plate separation of 3 mm is is 17.7 × 10⁻¹² F.
• A 12 pF capacitor connected to a 50 V battery has an electrostatic energy of 1.5 × 10⁻⁸ J stored in it.

Capacitors

• A capacitor of capacitance C = 900 pF charged fully by a 100 V battery and then connected to an uncharged capacitor of the same capacitance (900 pF) stores 2.25 x 10^-6 J of electrostatic energy.
• The charge passing through a conductor carrying current is given by Q = 5t² + 3t + 1; the current passing in the 5th second is 53 A.
• For a charge of 2 × 10^-2 C moving at 30 revolutions per second on a circle of diameter 80 cm, the current linked with the circuit is 0.60 A.

Resistance

• Resistance of a conductor depends on type of material, temperature, and dimensions.
• Resistivity of a material does not depend on dimensions of the conductor.
• For wire dimensions L (length) and D (diameter), resistance will be maximum for a wire with dimensions 2L and D/2.
• Ohm's law for a good conductor is V = IR.

Magnetic Fields

• J = σE represents Ohm's law.
• Increasing the temperature of a conductor may increase or decrease the product of its resistivity (ρ) and conductivity (σ).
• Two wires of equal lengths made of copper and manganin have the same resistance, the copper wire is thicker.
• The resistance for a conducting wire where the V → I graph is shown in figure given below will be tan50°.
• If the number density of free electrons in a wire is n, its area of cross-section is A, and drift velocity of electrons is vd, then electric current formed in this wire is nevd.
• The drift velocity of electrons is in the direction opposite to that of electric field.
• Kirchhoff's junction law shows the conservation of charge.
• Kirchhoff's second law is based on conservation of energy.
• When a battery is connected across a parallel combination of two unequal resistances, the p.d. across both the resistances would be equal.
• When a battery is connected across a series connection of two unequal resistances, the current passing through both the resistances would be equal.

Equivalent Resistance

• Equivalent resistance of series combination of two conducting wires is 14Ω and that of parallel combination of the same wires is 3.43 Ω; the high magnitude wire has resistance of 8 Ω.

Wheatstone Bridge

• A Wheatstone's Bridge measures resistance.
• In the circuit, if potential at point B is zero (VB = 0), then potential at points A and D will be +1.5 V and +2 V, respectively.

Maximum Power

• Maximum power that can be obtained from a battery of emf ε and internal resistance r connected with an external resistance R is ε^2 / 4r.

Electric Bulb

• If current increases by 1% in an electric bulb (with resistance of the filament of a bulb remaining constant) then the change in the power of a bulb increases by 2%.
• If the current flowing through a 2 Ω resistor is 3 A, the power consumed by a 5 Ω resistor is 1 W.

Ratio Of Power

• The rate of heat production in a conducting wire is proportional to l^2ρl / πr^2.
• If three cells each of emf 1.5 V and internal resistance 1 Ω connected in parallel, have emf 1.5 V.
• If 'n' number of cells having emf 'e' are connected in parallel, equivalent emf of the combination will bee.

Refraction

• In uniform magnetic field B = i + 2j + 3k, a particle moves in the x direction, the force acting on it will be in ZY plane.
• The formula for the magnetic field intensity B is [MT^-2A^-1].
• If the speed of a charged particle moving through a magnetic field is increased, then the trajectory will increase.
• As Coulomb's law is important in static electricity, Bio-Savart's law is important in magnetism.
• Ampere's circuital law is true for steady currents.

Magnetic Field

• Magnetic fields at points P and Q are directed at P and at Q.
• Magnetic field at 10 cm from an extremely long current carrying straight wire is 10^-5 Wb/m², the current passing through this wire is 5 A.
• A Helium nucleus revolves in a circular orbit of radius 0.8 m, magnetic field produced at the centre would be 5 x 10^-19 μο T.
• An extremely long straight wire, with radius of cross-section a, carries current I. The ratio of magnetic fields at distances a/2 and 2a from its axis would be 1.

Magnetic field produced at the centre of circular coil

• The magnetic field produced at the centre of a circular coil having radius 0.1 m and 2 turns if, A is the current that passes through it.
• Magnetic field due to a ring having n turns at a distance x on its axis is proportional to nr^2 / (x^2 + r^2)^(3/2) (where r = radius of ring).
• At a distance of 10 cm from a long straight wire carrying current, the magnetic field is 0.04 T, at the distance of 40 cm, the magnetic field will be 0.01T.
• For a solenoid of length 40 cm having 5000 turns, if 10 A of electric current passes through it the Magnetic field produced inside it is 0.0157 T
• If a current of 6 A passes through the wire as depicted in the questions figure, with Radius is 0.2 m (μ₀ = 4π × 10⁻⁷ Tm A⁻¹); Find: The magnitude of magnetic field at point C is zero.

Force

• If force F acts on two current carrying wires kept parallel. If current in one of the wires is made double and then the force acting between them becomes 2F.
• A current carrying loop is placed in a uniform magnetic field and the magnetic field acting it does not depend on the shape of the loop.
• For a rectangular coil 20 cm × 20 cm with 100 turns and carries a 1 A current is placed in a uniform magnetic field B = 0.5T with the direction of magnetic field parallel to the plane of the coil the magnitude of the torque required to hold this coil in this position is Zero.
• The dipole moment of a coil is 2i+3+5k. and the torque acting on it is√117 Nm.

Resistors

• If a very resistors, and in series, then the range of a voltmeter becomes increases.
• In order to increase the sensitivity of a moving coil galvanometer, the torsion constant of a spring should be decreased.

Alpha and Beta Particles

• When a charged particle enters a uniform magnetic field the path followed by it is circular .
• If a very long solenoid of length L has n layers and N turns in each layer (Given that Diometer is D and also canies current as I) then the magnetic field at the centre of the solenoid directly proportional to D
• The quantity known as current sensitivity of a galvanometer is Current per minute and angular deflection
• The resistance should be made smaller and there should be parallel to turn the galvanometer into an Ammeter.
• It is required to increase through smaller resistance should in join and parallel.
• The resistance of a coil is given by is (RG/ n-1) and the value is increase to make into the desired range S which can be expressed as: RG
• If the tightly bound 100 turn coil 10 cm for of radium when it is caring current of  1 Amps then what is the Magnetic flux at in the centre: 6.28× 10-⁴T
• If an ammeter is 0.2% of Main current passes through is 1/499G
• The ratio of radiuses of their part if the ionizedhydrogen and α - particles are : 2: 1

Solenoid

• At the centre the value of a long solenoid of 50 cm length having 100 turns and a carries ( the value is (µ₀ = 4π × 10⁷ Tm/amp A
• a very long is . straight wire of radiuses if current I and length is the point line and intensity of Magnetic Field is .

Lorentz Force

• The formula for the Lorentz force is F = qE + v * B is from the following.
• The force act between two between two is 1M and has equal of magnitude and vacuum.
• In axial ,Bar magnet is is .
• If the net charge zero then it can be .
• Formula unit to derive unit and is . Torque is .
• formula to express of magnetism equation is 1

Explore the fundamentals of electrostatics, including static charge, conductors, and the Coulomb. Understand the behavior of charged objects, the SI unit of charge (Coulomb), and attractive/repulsive forces. Review Coulomb's law and its applications.