Motional EMF in an Open Conductor

Q. There are two frictionless conducting rails placed in a transverse uniform magnetic field $B$ as shown in the figure. The rails are connected by a fixed capacitive arm $AB$ and a movable conducting rod $PQ$ is also placed as shown. If the rod $PQ$ is given a rightward initial velocity $V$ then the graph that best represents variation of speed of rod as a function of time

1. 
2. 
3. 
4. 

Q. A system consists of a thin charged wire ring of radius R and a very long uniformly charged thread oriented along the axis of the ring with one of its ends coinciding with the centre of ring. The total charge of the ring is equal to Q.The charge of the thread (per unit length) is equal to $\lambda$. Find the force of interaction between the ring and the thread.

1. $\frac{\lambda Q}{2\pi {ϵ}_{0}R}$
2. Zero
3. $\frac{\lambda Q}{\pi {ϵ}_{0}R}$
4. $\frac{\lambda Q}{4\pi {ϵ}_{0}R}$

Q.

Is resistance directly proportional to heat?

Q.

The magnitude of magnetic field (in $SIunits$) at the center of a hexagonal shape coil of side$10cm,50$ turns and carrying current $I\left(Ampere\right)$ in units of$\frac{{\mu }_{0}I}{\pi }$ is

1. $250\sqrt{3}$

2. $50\sqrt{3}$

3. $500\sqrt{3}$

4. $5\sqrt{3}$

Q.

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

1. $\frac{(\pi r^2\omega B{)}^2}{8R}$

2. $\frac{\pi r^2\omega B}{2R}$

3. $\frac{(\pi r\omega B{)}^2}{2R}$

4. $\frac{(\pi r{\omega }^{2}B{)}^2}{8R}$

Q. An aluminum ring $\text{B}$ faces an electromagnet $\text{A}$. The current through $\text{A}$ can be altered. Then which of the following statements is correct:

1. If current decreases, $\text{A}$ will repel $\text{B}$
2. Whether current increases or decreases, $\text{B}$ will not experience any force
3. If current increases, $\text{A}$ will repel $\text{B}$
4. If current increases, $\text{A}$ wil attract $\text{B}$

Q. A uniform magnetic field exists in the region given by $\overrightarrow{B}=3\hat{i}-5\hat{k}$. A rod of length $5m$ placed along $y-$axis is moved along $x-$axis with constant speed $1m{s}^{-1}$. Then induced emf in the rod is

1. Zero
2. $5V$
3. $10V$
4. $25V$

Q. A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement(s) from the following

1. The entire rod is at the same electric potential
2. There is an electric field in the rod
3. The electric potential is highest at the centre of the rod and decreases towards its ends
4. The electric potential is lowest at the centre of the rod and increases towards its ends

Q. A conductor of resistance $3\Omega$ is moving with speed v = 6 m/s. B is uniform & is equal to 4 Tesla. Length of the conductor is 50 cm. If $R=5\Omega$, find the power dissipated in $5\Omega$.

1. 6 Watt
2. 15 Watt
3. 9 Watt
4. 11 Watt

Q.

A player with 3 m long iron rod is running towards east with a speed of 30 km/hr. Horizontal component of earths magnetic field is $4$ x ${10}^{-5}Wb/m^2$. If he is running with rod in horizontal and vertical positions, then the potential difference induced across the ends of the rod in each of the cases would be

1. Zero in both cases

2. Zero in vertical position and in horizontal position

3. in vertical position and zero is horizontal position

4. in both cases

Q. A very long solenoid of radius $R$ is carrying current $I\left(t\right)=kt{e}^{-\alpha t}(k>0),$ as a function of time $(t\ge 0).$ Counterclockwise current is taken to be positive. A circular conducting coil of radius $2R$ is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by-

1. 
2. 
3. 
4. 

Q.

Figure shows a suare loop of side 5 cm being moved towards right at a constant speed of 1 cm.s. The front edge enters the 20 cm wide magnetic field at t= 0. Find the emf induced in the top at

(a) t = 2 s,

(b) t = 10 s,

(c) t = 22 s. and

(d) t = 30 s.

Q. Match List-I with List-II

List-I	List-II
$\left(a\right)$ Capacitance, $C$	$\left(i\right)M^1{L}^1{T}^{-3}{A}^{-1}$
$\left(b\right)$ Permitivity of free space, ${ϵ}_0$	$\left(ii\right)M^{-1}{L}^{-3}{T}^4{A}^2$
$\left(c\right)$ permeabilityof free space, ${\mu }_0$	$\left(iii\right)M^{-1}{L}^{-2}{T}^4{A}^2$
$\left(d\right)$ electric field, $E$	$\left(iv\right)M^1{L}^1{T}^{-2}{A}^{-2}$

Choose the correct answer from the options given below.

1. $\left(a\right)\to \left(iii\right),\left(b\right)\to \left(ii\right),\left(c\right)\to \left(iv\right),\left(d\right)\to \left(i\right)$
2. $\left(a\right)\to \left(iii\right),\left(b\right)\to \left(iv\right),\left(c\right)\to \left(ii\right),\left(d\right)\to \left(i\right)$
3. $\left(a\right)\to \left(iv\right),\left(b\right)\to \left(ii\right),\left(c\right)\to \left(iii\right),\left(d\right)\to \left(i\right)$
4. $\left(a\right)\to \left(iv\right),\left(b\right)\to \left(iii\right),\left(c\right)\to \left(ii\right),\left(d\right)\to \left(i\right)$

Q. Explain the construction and working of a moving coil galvanometer?

Q.

What is the value of $-3$ to the power $-4$?

Q. The radius of the circular conducting loop shown in figure is $R$. Magnetic field is decreasing at a constant rate $\alpha$. Resistance per unit length of the loop is $\rho$. Then current in wire $AB$ is ($AB$ is one of the diameters)

1. $\frac{R\alpha }{2\rho }$ from $A$ to $B$
2. $\frac{R\alpha }{2\rho }$ from $B$ to $A$
3. $\frac{2R\alpha }{\rho }$ from $A$ to $B$
4. $\text{zero}$

Q.

An aeroplane in which the distance between the tips of wings is 50 m is flying horizontally with a speed of 360 km/hr over a place where the vertical component of earth's magnetic field is $2.0$ x ${10}^{-4}weber/m^2$ . The potential difference between the tips of the wings would be

1. 0.1 V

2. 1.0 V

3. 0.2 V

4. 0.01 V

Q. A circular coil of wire of radius $r$ has $n$ turns and carries a current $i$. The magnetic induction $\left(B\right)$ at a point on the axis of the coil at a distance $\sqrt{3}r$ from its center is-

1. $\frac{{\mu }_{0}ni}{4r}$
2. $\frac{{\mu }_{0}ni}{8r}$
3. $\frac{{\mu }_{0}ni}{16r}$
4. $\frac{{\mu }_{0}ni}{32r}$

Q.

Why galvanometer is not used in AC bridges?

Q. 80.To make the magnetic field radial in a moving coil galvanometer 1) the number of turns in tje coil is increased 2) magnet is taken in the form of horse shoe 3) poles are cylindrically cut 4)coil is wound on aluminum frame

Q. The $E-r$ curve for an infinite linear charge distribution will be

1. 
2. 
3. 
4. 

Q. As shown in the figure, if the value of $rms$ current is $2.2\text{A}$, the power factor of the box is

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

Q.

The potential difference between points A and B in the given figure is?

Q.

Figure shows a wire sliding on two parallel, condu cting rails placed at a separation l. A magnetic field B exicts in a direction perpendicular to the plane of the rails. What force is necessary to keep the wire moving at a constant velocity v ?

Q. A rectangular conductor LMNO is placed in a uniform magnetic field of $0.5T$. The field is directed perpendicular to the plane of the conductor. When the arm $MN$ of length of $20cm$ is moved towards left with a velocity of $10m{s}^{-1}$, calculate the emf induced in the arm. Given the resistance of the arm to be $5\Omega$, (assuming that other arms are of negligible resistance) find the value of the current in the arm.

Q. (a) An iron ring of relative permeability ${\mu }_r$ has windings of insulated copper wire of n turns per metre. When the current in the windings is I, find the expression for the magnetic field in the ring.
(b) The susceptibility of a magnetic material is 0.9853. Identify the type of magnetic material. Draw the modification of the field pattern on keeping a piece of this material in a uniform magnetic field.

Q. A solid conducting sphere of radius $10\text{cm}$ is enclosed by a thin metallic shell of radius $20\text{cm}$. A charge $q=20\mu \text{C}$ is given to the inner sphere. Find the heat generated in the process, the inner sphere is connected to the shell by a conducting wire-

Q. The surface charge density of a ring of radius $a$ and thickness $d$ is $\sigma$ as shown in figure. If rotates with a frequency $f$ about an axis passing through its centre and perpendicular to its plane. Assume that charge is present only on the outer surface. The magnetic field induction at a point $\text{P}$ on axis at a very large distance $L$ from its centre will be:
$[$Assume that $(d<<a)]$

1. $\frac{\pi {\mu }_0\sigma df}{L^2}$
2. $\frac{\pi {\mu }_0{\sigma }^{2}adf}{L^3}$
3. $\frac{\pi {\mu }_0\sigma dfa}{L^3}$
4. $\frac{\pi {\mu }_0{a}^{3}d\sigma f}{L^3}$

Q.

How can we define an ampere using the concept of the force between two infinitely long parallel current carrying conductors?

Q. If the number of turns in armature is made twice current 3 times and B - 4 times and area of armature is made half then speed of the motor becomes