Three identical coils $C_1, C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly midway. $C_1$ carries current $I$ in anti-clockwise direction while $C_3$ carries current $I$ in clockwise direction. An induced current flows through $C_2$ will be in clockwise direction when

A conducting circular loop of area $1.0 \mathrm{~m}^2$ is placed perpendicular to a magnetic field which varies as $B=\sin (100 t)$ Tesla. If the resistance of the loop is $100 \Omega$, then the average thermal energy dissipated in the loop in one period is $\_\_\_\_$ J.

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T . If the resistance of the total circuit is $2 \Omega$ then the force needed to move the rod towards right with constant speed $(v)$ of $1.5 \mathrm{~m} / \mathrm{s}$ is $\_\_\_\_$ N.

A coil of area A and N turns is rotating with angular velocity $\omega$ in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $\vec{B}$. Magnetic flux $\varphi$ and induced emf $\varepsilon$ across it, at an instant when $\vec{B}$ is parallel to the plane of coil, are :