Embibe Experts Solutions for Chapter: Electromagnetic Induction, Exercise 1: Uttar Pradesh Board-2018

Define coefficient of self-inductance.

Write down the definition and unit of coefficient of mutual induction. Derive the formula of mutual inductance between two plane coils.

Write the Faraday's laws of electromagnetic induction. $\mathrm{A}$ copper rod of length $\mathrm{l}$ is rotating about its one end with angular velocity $\mathrm{\omega }$ in a plane perpendicular to a uniform magnetic field intensity $\mathrm{B}$. Prove that induced electromotive force between the ends of rod will be $\mathrm{e}=\frac{1}{2}{\mathrm{\omega Bl}}^2$.

In the given figure, the value of current is increasing in the wire $\mathrm{AB}$ from $\mathrm{A}$ to $\mathrm{B}$. If there is any induced current in the loop, then what should be its direction?

The current in an inductor is given by $\mathrm{i}=5+16\mathrm{t}$, where $\mathrm{i}$ and $\mathrm{t}$ are in ampere and second respectively. The induced $\mathrm{emf}$ is $10 \mathrm{mV}$. Find out $\left(\mathrm{i}\right)$ self-inductance and $\left(\mathrm{ii}\right)$ the energy stored in the inductor at $\mathrm{t}=1$ second.

Define $1$ henry of self inductance.

Define coefficient of mutual induction. A circular coil $\mathrm{X}$of radius $0.02 \mathrm{m}$ and $100$ turns is placed coaxially and concentric with another coil $\mathrm{Y}$of radius $0.2 \mathrm{m}$, having $1000$turns. Find mutual inductance of the coils, when current in the coil $\mathrm{Y}$changes from $7\mathrm{A}$ to $5\mathrm{A}$ in $4\times {10}^{-2} \mathrm{s}$. What is the $\mathrm{e}.\mathrm{m}.\mathrm{f}.$ induced in the coil $\mathrm{X}$?