The magnetic flux linked with a coil at any instant $t$ is given by $\phi = 5t^3 - 100t + 300$. The $e.m.f.$ induced in the coil at $t = 2 \ s$ is $....... \ V$.

$A$ flexible circular loop $20 \ cm$ in diameter lies in a magnetic field of magnitude $B = 1 \ T$,directed into the plane of the page as shown. The loop is pulled at the points indicated by the arrows,forming a loop of zero area in $0.314 \ s$. The average emf induced in the loop is.....$V$

Statement $-1$: When a magnet is made to fall freely through a closed coil,its acceleration is always less than acceleration due to gravity $(g)$.
Statement $-2$: Current induced in the coil opposes the motion of the magnet,as per Lenz's law.

$A$ square wire loop of $10.0 \, cm$ side lies at right angles to a uniform magnetic field of $20 \, T$. $A$ $10 \, V$ light bulb is in series with the loop as shown in the figure. The magnetic field is decreasing steadily to zero over a time interval $\Delta t$. The bulb will shine with full brightness if $\Delta t$ is equal to.......$ms$.

$A$ circular coil has $100$ turns,radius $3 \ cm$ and resistance $4 \Omega$. This coil is co-axial with a solenoid of $200$ turns/cm and diameter $4 \ cm$. If the solenoid current is decreased from $2 \ A$ to zero in $0.04 \ s$,then the current induced in the coil is

An electron moves on a straight line path $XY$ as shown. The $abcd$ is a coil adjacent to the path of the electron. What will be the direction of current,if any,induced in the coil?