S L Arora Solutions for Chapter: Electromagnetic Induction, Exercise 7: Text Based Exercises

When is the magnetic flux taken as negative?

A rectangular coil of area $A$, having number of turns $N$ is rotated at ‘$f$’ revolutions per second in a uniform magnetic field $B$, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is $2\pi f NBA$.

Or

A coil of number of turns $N$, area $A$ is rotated at a constant angular speed $\omega$ in a uniform magnetic field $B$ and connected to a resistor $R$. Deduce expressions for:  Power dissipation in the coil.

Deduce an expression for the self-inductance of a long solenoid of $N$ turns, having a core of relative permeability ${\mu }_r$.

Define mutual inductance and write its SI units.

Derive an expression for the mutual inductance of two long co-axial solenoids of same length wound one over the other.

In an experiment, two coils $C_1$ and $C_2$ are placed close to each other. Find out the expression for the emf induced in the coil $C_1$ due to a change in the current through the coil $C_2$.

When a bar magnet is pushed towards (or away) from the coil connected to a galvanometer, the pointer in the galvanometer deflects. Identify the phenomenon causing this deflection and write the factors on which the amount and direction of the deflection depends. State the laws describing this phenomenon.

Sketch the change in flux, emf and force when a conducting rod $PQ$ of resistance $R$ and length $l$ moves freely to and fro between $A$ and $C$ with speed $v$ on a rectangular conductor placed in uniform magnetic field as shown in the figure.