Electromagnetism

Capacitance of a parallel plate capacitor:
where , , .
Answer: 1.77 pF.

Induced emf due to mutual inductance:
Given: , .
Answer: 70 mH.

For parallel cells with emf , , , , equivalent emf:
Equivalent internal resistance:
Total resistance: .
Current through external resistance:
Answer: .

A conductor of length moving with velocity perpendicular to a uniform magnetic field induces an emf due to motional electromotive force.
Assume conductor along y-axis, magnetic field along z-axis, velocity along x-axis.
The induced emf is: derived from Lorentz force on charges: .
For perpendicular motion, the effective force separates charges, creating a potential difference .
Answer: .

Magnetic field due to a long straight wire:
where , , .
Answer: .

Magnetization ( ): The magnetic moment per unit volume of a material, induced by an external magnetic field. , unit: A/m.
Magnetic Intensity ( ): The magnetizing force or magnetic field strength that induces magnetization in a material. in vacuum, unit: A/m.
Magnetic Susceptibility ( ): A measure of how a material becomes magnetized in an external magnetic field. , dimensionless.
Answer: Magnetization is magnetic moment per volume; magnetic intensity is magnetizing force; susceptibility is response to field.

a. Inductive Reactance ( ): The opposition offered by an inductor to alternating current, given by , where is inductance and is frequency. Unit: ohm.
b. Capacitive Reactance ( ): The opposition offered by a capacitor to alternating current, given by , where is capacitance. Unit: ohm.
c. Impedance ( ): The total opposition to alternating current in a circuit with resistance, inductance, and capacitance, given by . Unit: ohm.
Answer: Inductive reactance opposes current in inductors; capacitive in capacitors; impedance is total AC opposition.

Resonant frequency of an LCR series circuit: where , .
Answer: .

Potentiometer:
1. Measures potential difference without drawing current from the circuit, using a null point method.
2. Provides high accuracy as it balances the unknown voltage against a known voltage gradient.
Voltmeter:
1. Measures potential difference by drawing a small current, as it is connected in parallel.
2. Less accurate due to its finite resistance, which affects the circuit.
Answer: Potentiometer measures voltage at null point without current draw, offering higher accuracy; voltmeter draws current and is less accurate.

Polar Dielectrics: These are materials with molecules that have a permanent electric dipole moment due to an asymmetric charge distribution (e.g., water, HCl). In the absence of an electric field, dipoles are randomly oriented, but they align partially in an external field, enhancing polarization.
Non-Polar Dielectrics: These are materials with molecules that have no permanent dipole moment, as charges are symmetrically distributed (e.g., O , benzene). Polarization occurs only in an external electric field due to induced dipoles from charge displacement.
Answer: Polar dielectrics have permanent dipole moments; non-polar dielectrics have no permanent dipoles but can be polarized by an external field.

For inductors in series, the total inductance is the sum of individual inductances: Given: , .
Answer: 30 mH.

The potential gradient of a potentiometer wire is the rate of change of potential difference per unit length along the wire. It is denoted by and is given by , where is the potential difference across the wire and is the length of the wire. The unit is volts per meter (V/m).
Answer: The potential gradient is the potential difference per unit length of the potentiometer wire, expressed as (unit: V/m).

The unit of magnetic flux is the weber (Wb). Magnetic flux density is flux per unit area: Thus, Wbm is a typo for Wb/m , which is tesla.
Answer: tesla.

Torque on an electric dipole in a uniform electric field is , where is the dipole moment, is the electric field strength, and is the angle between the dipole and the field. Maximum torque occurs when , i.e., .
Answer: .

Alternating current (AC) is sinusoidal, typically . Over one full cycle, the positive and negative halves cancel out, resulting in an average value of zero.
Answer: zero.