Academic Experts Solutions for Chapter: Electromagnetic Induction, Exercise 10: Motion EMF Due to Rotation

In a uniform magnetic field of induction $B$, a wire in the form of semicircle of radius $r$, rotates about the diameter of the circle with angular frequency $\omega$. If the total resistance of the circuit is $R$, the mean power generated per period of rotation is 

A metal conductor of length $1 \mathrm{m}$ rotates in a vertical plane about one of its ends at angular velocity $5 \mathrm{rad} {\mathrm{s}}^{-1}$. If the horizontal component of earth's magnetic field is $0.2\times {10}^{-4} \mathrm{T}$, then the emf developed between the two ends of the conductor is 

A conducting ring of radius $r$, with a conducting spoke, is in pure rolling, on a horizontal surface, in a region having a uniform magnetic field $\overrightarrow{B}$, as shown. If $v$ is the velocity of the centre of the ring, then, the potential difference $V_O-V_A$ is 

A wooden stick of length $3l$ is rotated about an end with a constant angular velocity $\omega$ in a uniform magnetic field $B$ perpendicular to the plane of motion. If the upper one-third of its length is coated with copper, find the potential difference across the whole length of the stick. 

When a $J$ shaped conducting rod is rotating in its own plane with a constant angular velocity $\omega$, about one of its end $p$, in a uniform magnetic field $\overrightarrow{B}$, directed normally into the plane of paper, then, the magnitude of emf induced across it will be

The figure shows a rod of length $l$ with points $A$ and $B$ on it. The rod is moved in a uniform magnetic field $\left(B_0\right)$ in different ways as shown. In which case, the potential difference $\left(V_A-V_B\right)$ between $A$ and $B$ is minimum?

A bent rod $PQR$ $\left(PQ=QR=l\right)$ shown here is rotating about its end $P$ with an angular speed $𝝎$ in a region of transverse magnetic field of strength $B$. Then

Induced emf produced in a coil, rotating about its diameter with constant angular velocity and axis (diameter) perpendicular to a uniform magnetic field, will be maximum when the angle between the plane of the coil and the direction of magnetic field is