Embibe Experts Solutions for Chapter: Electromagnetic Induction, Exercise 1: WBJEE 2019

A conducting circular loop of resistance $20 \mathrm{\Omega }$ and cross-sectional area $20\times {10}^{-2} {\mathrm{m}}^2$ is placed perpendicular to a spatially uniform magnetic field $B$, which varies with time $t$ as $B=2\sin \left(50\pi t\right)\mathrm{T}$. Find the net charge flowing through the loop in $20 \mathrm{ms}$ starting from $t=0$.

A metallic loop is placed in a uniform magnetic field $B$ with the plane of the loop perpendicular to $B.$ Under which condition (s) given an emf will be induced in the loop? "If the loop is .....

A square conducting loop is placed near an infinitely long current-carrying wire with one edge parallel to the wire as shown in the figure. If the current in the straight wire is suddenly halved, which of the following statements will be true?
"The loop will "
 

As shown in the figure, a rectangular loop of a conducting wire is moving away with a constant velocity $v$ in a perpendicular direction from a very long straight conductor carrying a steady current $I$. When the breadth of the rectangular loop is very small compared to its distance from the straight conductor, how does the emf: $E$induced in the loop vary with time $t ?$

Consider a conducting wire of length $L$ bent in the form of a circle of radius $R$ and another conductor of length $a\left(a<<R\right)$ is bent in the form of a square. The two loops are then placed in same plane such that the square loop is exactly at the centre of the circular loop. What will be the mutual inductance between the two loops?

When a $\mathrm{DC}$ voltage is applied at the two ends of a circuit kept in a closed box, it is observed that the current gradually increases from zero to a certain value and then remains constant. What do you think that the circuit contains?