Embibe Experts Solutions for Chapter: Electromagnetic Induction, Exercise 1: Exercise - 1

A choke coil is preferred to a rheostat in AC circuit as,

A bicycle is resting on its stand in the east-west direction and the rear wheel is rotated at an angular speed of $100 \mathrm{rpm}$. If the length of each spoke is $30.0 \mathrm{cm}$, and the horizontal component of the earth's magnetic field is $2.0\times {10}^{-5} \mathrm{T}$, find the emf induced between the axis and the outer end of a spoke. Neglect centripetal force acting on the free electrons of the spoke.

The current in an ideal, long solenoid is varied at a uniform rate of $0.01 \mathrm{A} {\mathrm{s}}^{-1}$. The solenoid has $2000 \mathrm{turns} {\mathrm{m}}^{-1}$ and its radius is $6.0 \mathrm{cm}$. $\left(a\right)$ Consider a circle of radius $1.0 \mathrm{cm}$ inside the solenoid with its axis coinciding with the axis of the solenoid. Write the change in the magnetic flux through this circle in $2.0 \mathrm{s}$ $\left(b\right)$ Find the electric field induced at a point on the circumference of the circle. ($\left(c\right)$ Find the electric field induced at a point outside the solenoid at a distance $8.0 \mathrm{cm}$ from its axis.

The mutual inductance between two coils is $2.5 \mathrm{H}$. If the current in one coil is changed at the rate of $1 \mathrm{A} {\mathrm{s}}^{-1}$, what will be the emf induced in the other coil?

A uniform magnetic field exists in region given by $\overrightarrow{B}=\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}+5\hat{\mathrm{k}}\right) \mathrm{T}$. A rod of length $5 \mathrm{m}$ is placed along $y$ axis is moved along $x$- axis with constant speed $1 \mathrm{m} {\mathrm{s}}^{-1}$. Then induced $e.m.f.$ in the rod will be:

A rod of length $l$ rotates with a small but uniform angular velocity $\omega$ about its perpendicular bisector. A uniform magnetic field of $0.3 \mathrm{T}$ exists parallel to the axis of rotation. The potential difference between the two ends of the rod is-

In a series $L-R$ growth circuit, if maximum current and maximum induced emf in an inductor of inductance $3 \mathrm{mH}$ are $2 \mathrm{A}$ and $6 \mathrm{V}$ respectively, then the time constant of the circuit is :

A long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is