Rotational EMF

Q.

A long straight wire of radius $a$ carries a steady current $i$. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ from its axis is

Q. A 250-turn rectangular coil of length $2.1cm$ and width $1.25cm$ carries a current of 85 $\mu A$ and subjected to a magnetic field of strength $0.85T$. Work done in rotating the coil by ${180}^0$ against the torque is

1. $9.4\mu J$
2. $2.3\mu J$
3. $1.15\mu J$
4. $9.1\mu J$

Q. The electric field of a plane electromagnetic wave is given by
$\overrightarrow{E}=E_0\frac{\hat{i}+\hat{j}}{\sqrt{2}}\cos (kz+\omega t)$
At $t=0$, a positively charged particle is at the point $(x,y,z)=(0,0,\frac{\pi }{k})$. If its instantaneous velocity at $(t=0)$ is $v_0\hat{k}$, the force acting on it due to the wave is:

1. parallel to $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$
2. zero
3. antiparallel to $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$
4. parallel to $\hat{k}$

Q.

In the circuit, given in the figure currents in different branches and the value of one resistor are shown. Then potential at point B with respect to point A is:

1. $+2\mathrm{V}$

2. $-2\mathrm{V}$

3. $+1\mathrm{V}$

4. $-1\mathrm{V}$

Q. The bob of a simple pendulum has mass $2g$ and a charge of $5.0\mu C$. It is at rest in a uniform horizontal electric field of intensity $2000V/m$. At equilibrium, the angle that the pendulum makes with the vertical is (take $g=10m/s^2)$.

1. ${\tan }^{-1}\left(5.0\right)$
2. ${\tan }^{-1}\left(2.0\right)$
3. ${\tan }^{-1}\left(0.5\right)$
4. ${\tan }^{-1}\left(0.2\right)$

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

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

Q.

The dimension of$B^2/2{\mu }_0$where $B$ is magnetic field and ${\mu }_0$ is the magnetic permeability of vacuum, is

1. $\left[M{L}^{-1}{T}^{-2}\right]$

2. $\left[M{L}^2{T}^{-2}\right]$

3. $\left[ML{T}^2\right]$

4. $\left[M{L}^2{T}^{-1}\right]$

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. 50 μV
2. 50 mV
3. 5x10^-4 V
4. 5 mV

Q. List Match Set-I

In each situation of Column - I, two electric dipoles having dipole moments $p_1$ and $p_2$ of same magnitude (that is, $p_1=p_2$) are placed on $x-$axis symmetrically about origin in different orientations are shown. In Column - II certain inferences as drawn fro these two dipoles. Then match the different orientations of dipoles in Column - I with the corresponding resulting in Column – II

	Column-I		Column-II
(A)	(${\overrightarrow{P}}_1\text{and}{\overrightarrow{P}}_2$ are perpendicular to x-axis as shown)	(P)	The torque on one dipole due to other is zero.
(B)	(${\overrightarrow{P}}_1\text{and}{\overrightarrow{P}}_2$ are perpendicular to x-axis as shown)	(Q)	The potential energy of one dipole in electric field of other dipole is negative
(C)	(${\overrightarrow{P}}_1\text{and}{\overrightarrow{P}}_2$ are Parallel)	(R)	There is one straight line in x-y plane (not at infinity) to x-axis as shown which is equipotential
(D)	(${\overrightarrow{P}}_1\text{and}{\overrightarrow{P}}_2$ are perpendicular to x-axis as shown)	(S)	Electric field at origin is zero.

Which of the following option has the correct combination considering column-I and column-II ?

1. $C-P,Q$
2. $D-P,R$
3. $B-P,Q,R,S$
4. $A-P,S$

Q. A square metal wire loop of side $10\text{cm}$ and resistance $1\Omega$ is moved with a constant velocity $v$ in uniform magnetic field $B=2\text{T}$ as shown in Fig. The magnetic field is perpendicular to the plane of the loop and directed into the paper. The loop is connected to a network of resistors, each equal to $3\Omega$. What should be the speed of the loop so as to have a steady current of $1\text{mA}$ in the loop?

1. $1\text{cm/s}$
2. $2\text{cm/s}$
3. $3\text{cm/s}$
4. $4\text{cm/s}$

Q.

The unit of reduction factor of tangent galvanometer:

1. Gauss

2. Ampere

3. Radian

4. None Of These

Q.

The magnetic flux across a loop of resistance $10\Omega$ is given by $ɸ=5t^2–4t+1$ weber. How much current is induced in the loop after $0.2$sec?

1. $0.4A$

2. $0.2A$

3. $0.04A$

4. $0.02A$

Q.

Calculate the smaller force if the bigger force is $40\mathrm{N}$ and the resultant force is perpendicular to the smaller force. The two forces are acting at an angle of ${120}^{\circ }$

Q. An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?

1. They will come out travelling along parallel paths
2. They will come out at the same time
3. They will come out at different times
4. They will never come out of the magnetic field region

Q. Two conducting rings $P$ and $Q$ of radii $r$ and $2r$ rotate uniformly in opposite directions with centre of mass velocities $2v$ and $v$ respectively on a conducting surface $S$. There is a uniform magnetic field of magnitude $B$ perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is

1. Zero
2. $16Bvr$
3. $4Bvr$
4. $8Bvr$

Q. A square loop of side $a$ hangs from an insulating hanger of spring balance. The magnetic field of strength $B$ occurs only at the lower edge. It carries a current $I$. Find the change in the reading of the spring balance if the direction of current is reversed

1. $\frac{IaB}{2}$
2. $\frac{3}{2}IaB$
3. $2IaB$
4. $IaB$

Q.

A copper rod of length l is rotated about one end perpendicular to the magnetic field B with constant angular velocity ω. The induced e.m.f. between the two ends is

1. 

2. 

3. 

4. 

Q. What is back emf in a DC motor?

Q. How to calculate spin only magnetic moment explain

Q. A metallic disc of radius R is rotating about its geometrical axis with constant angular speed w in external magnetic field B which is perpendicular to the plane of the disc then induced emf between the centre and any peripheral point of the disc is given by :- (1) wBR^2*pi (2) wBR^2 (3) wBR^2*pi/2 (4) wBR^2/2

Q. The magnetic field in a region of space varies according to the equation$\overrightarrow{B}=B_0[x\hat{i}+y\hat{j}+\hat{k}]$. The magnetic flux associated with the area bounded by the line $x=0,y=0,x=a$ and $y=\frac{b}{2}$ in the $x-y$ plane is

1. $\text{zero}$
2. $B_{0}ba$
3. $\frac{3B_{0}ba}{2}$
4. $\frac{B_{0}ba}{2}$

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

Q. A 1.0 m long metallic rod is rotated with an angular frequency of400 rad s–1 about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallicring. A constant and uniform magnetic field of 0.5 T parallel to theaxis exists everywhere. Calculate the emf developed between the centre and the ring.

Q.

A conducting disc of radius r rotates with a small but constant angular velocity w about its axis. A uniform magnetic field B exists parallel to the axis of rotation. Find the motional emf between the centre and the periphery of the disc.

Q.

A bullet is fired from a canon with velocity 500 m/s. If the angle of projection is ${15}^{\circ }$ and $g=10m/s^2$. Then the range is

1. 

2. 

3. 

4. 

Q. An electron and a proton are moving on straight parallel paths with same velocity. The enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true ?

1. They will never come out of the magnetic field region
2. They will come out travelling along parallel paths
3. They will come out at different times
4. They will come out at the same time

Q. A conducting rod AC of length $4l$ is rotated about a point 0 in a uniform magnetic field field $\overrightarrow{B}$ directed into the paper. $AO=l$ and $OC=3l$ , then

1. $V_A-V_0=\frac{B\omega l^2}{2}$
   
2. $V_0-V_C=\frac{7B\omega l^2}{2}$
   
3. $V_C-V_0=\frac{9B\omega l^2}{2}$
   
4. $V_A-V_C=4B\omega l^2$

Q. A copper disc of radius 0.1 m rotates about its centre with 10 revolutions per second in a uniform magnetic field of 0.1 Tesla. The emf induced across the radius of the disc is

1. 
2. 
3. 
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. $2B\omega R^2$