Rotational EMF

Q. A square coil of side 10 cm has 10 turns. It rotates in a magnetic field of induction 0.02 T and produces a maximum induced emf of 10 mV. Then the angular velocity of the coil is

1. $0.5rad{s}^{-1}$
2. $5rad{s}^{-1}$
3. $5\pi rad{s}^{-1}$
4. $0.2\pi rad{s}^{-1}$

Q.

Find the magnetic moment of a rotating rod of mass M, charge Q and length L rotating about an end point at $\omega rad{s}^{-1}$

1. $\frac{QW{L}^2}{6}$

2. $\frac{QW{L}^2}{3}$

3. $QW{L}^2$

4. $\frac{QW{L}^2}{2}$

Q. A conducting rod AC of length 4l is rotated about a point O in a uniform magnetic field $\overrightarrow{B}$ directed into the paper. AO = l and OC = 3l. Then

1. $V_A-V_O=\frac{B\omega l^2}{2}$
   
2. $V_O-V_C=\frac{7}{2}B\omega l^2$
   
3. $V_A-V_C=4B\omega l^2$
   
   
4. $V_C-V_O=\frac{9}{2}B\omega l^2$
   

Q. A conducting rod of length 2l is rotating with constant angular speed $\omega$ about its perpendicular bisector. A uniform magnetic field exists parallel to the axis of rotation. The e.m.f. induced between two ends of the rod is

1. $B\omega l^2$
   
2. $\frac{1}{2}B\omega l^2$
   
3. $\frac{1}{8}B\omega l^2$
   
4. Zero

Q. A quarter circular conducting ring of radius $r$ is rotating at angular velocity $\omega$ in uniform magnetic field as shown in figure.
EMF induced across the ring is

1. $B\omega R^2$
2. $\frac{B\omega R^2}{2}$
3. $\frac{B\omega R^2}{4}$
4. $2B\omega R^2$

Q. A rod of length L is rotating with an angular velocity $\omega$ in a uniform magnetic field $B_0$ as shown in figure. Potential difference between the ends of rod A and B is
(Take $OB=\frac{L}{4}$)

1. $B\omega L^2$
2. $\frac{B\omega L^2}{2}$
3. $\frac{B\omega L^2}{3}$
4. $\frac{B\omega L^2}{4}$

Q. A quarter circular conducting ring of radius $r$ is rotating at angular velocity $\omega$ in uniform magnetic field as shown in figure.
EMF induced across the ring is

1. $B\omega R^2$
2. $\frac{B\omega R^2}{2}$
3. $\frac{B\omega R^2}{4}$
4. $2B\omega R^2$

Q. A wire loop enclosing a semicircle of radius $R$ is located on the boundary of uniform magnetic field $B$. At time $t=0$, the loop is set into motion with constant angular accleration $\alpha$ about an axis passing through $O$ and is perpendicular to semicircle. The clockwise emf direction is taken to be positive. The modulus of variation of emf as a function of time is ($0<\theta <\pi$)

1. $\frac{B{R}^2\alpha t}{2}$
2. $\frac{3B{R}^2\alpha t}{2}$
3. $\sqrt{3}B{R}^2\alpha t$
4. $\frac{B{R}^2\alpha t}{\sqrt{2}}$

Q. A wire loop enclosing a semicircle of radius $R$ is located on the boundary of uniform magnetic field $B$. At time $t=0$, the loop is set into motion with constant angular accleration $\alpha$ about an axis passing through $O$ and is perpendicular to semicircle. The clockwise emf direction is taken to be positive. The modulus of variation of emf as a function of time is ($0<\theta <\pi$),
then the variation of emf as a function of time is given by the graph

1. 
2. 
3. 
4. 

Q. A conducting straight wire $PQ$ of length $l$ is fixed along a diameter of a non-conducting ring as shown in the figure. The ring is given a pure rolling motion on a horizontal surface such that its centre of mass has a velocity $v$. There exists a uniform horizontal magnetic field $B$ in horizontal direction perpendicular to the plane of ring. The magnitude of induced emf in the wire $PQ$ at the position shown in the figure will be

1. $Bvl$
2. $2Bvl$
3. $3Bvl/2$
4. $\text{Zero}$

Q. A rod of length L is rotating with an angular velocity $\omega$ in a uniform magnetic field $B_0$ as shown in figure. Potential difference between the ends of rod A and B is
(Take $OB=\frac{L}{4}$)

1. $B\omega L^2$
2. $\frac{B\omega L^2}{2}$
3. $\frac{B\omega L^2}{3}$
4. $\frac{B\omega L^2}{4}$

Q. Find the variation of ${ϵ}_{ind}$ vs time for the following system.

1. 
2. 
3. 
4. 

Q. A wheel having metal spokes of 1 m long between its axle and rim is rotating in a magnetic field of flux density $5\times {10}^{-5}$ T normal to the plane of the wheel. An e.m.f of $\frac{22}{7}mV$ is produced between the rim and the axle of the wheel. The rate of rotation of the wheel in revolutions per seconds is

1. 10
2. 20
3. 30
4. 40

Q. A metal conductor of length 1m rotates vertically about one of its ends at angular velocity 5 radians per second. If the horizontal component of earth's magnetic field is
$0.2\times {10}^{-4}T,$ then the e.m.f. developed between the two ends of the conductor is

1. 5 mV
2. $5\times {10}^{-4}$ V
3. 50 mV
4. 50$\mu$V