Shortcut Methods and Tricks to Solve Faraday’s Law of Induction Numericals

Mutual Inductance: a) Use the formula for mutual inductance: $$M=\frac{\mu_0N_1N_2\pi R^2}{l}$$ where: - (M) is the mutual inductance in henries (H).

• (\mu_0) is the permeability of free space ((4\pi \times 10^{-7}) H/m).
• (N_1) and (N_2) are the number of turns in the first and second coils, respectively.
• (R) is the radius of the coils in meters (m).
• (l) is the length of the coils in meters (m).

b) Use the formula for mutual inductance per unit length: $$L_{mut}=\frac{\mu_0N_1N_2}{2\pi d}\text{ H/m}$$ where: - (L_{mut}) is the mutual inductance per unit length in henries per meter (H/m).

• (d) is the distance between the wires in meters (m).

Self-Inductance: a) Use the formula for the self-inductance of a solenoid: $$L=\frac{\mu_0N^2A}{l}\text{ H,}$$ where: - (L) is the self-inductance in henries (H). - (\mu_0) is the permeability of free space ((4\pi \times 10^{-7}) H/m). - (N) is the number of turns in the solenoid. - (A) is the cross-sectional area of the solenoid in square meters (m²). - (l) is the length of the solenoid in meters (m).

b) Use the formula for the time constant of an inductor-resistor (L-R) circuit: $$\tau=\frac{L}{R}\text{ s}$$ where: - (\tau) is the time constant in seconds (s). - (L) is the inductance in henries (H). - (R) is the resistance in ohms ((\Omega)).

Lenz’s Law: a) Use Lenz’s law to determine the direction of the induced current in the coil such that it opposes the change in magnetic flux. The right-hand rule can be applied to find the direction of the induced current.

b) According to Lenz’s law, the induced current in the metal ring will oppose the change in magnetic flux. The direction of the induced current can be determined using the right-hand rule.

Applications: a) Explain the working principle of a transformer based on Faraday’s law of induction. Include a diagram and describe the process of electromagnetic induction in the transformer.

b) Describe how an inductor is used in an AC circuit to limit the flow of current. Explain the concept of inductive reactance and how it affects the current in an AC circuit.