EMI in One Equation

Q. A conducting rod $\text{PQ}$ of length $l=2\text{m}$ is moving at a velocity $v=8{\text{ms}}^{-1}$ making an angle ${30}^{\circ }$ with its length. A uniform magnetic field $B=3\text{T}$ exits in a direction perpendicular to the plane of motion. Then

1. $V_P-V_Q=41.6\text{V}$
2. $V_P-V_Q=24\text{V}$
3. $V_Q-V_P=41.6\text{V}$
4. $V_Q-V_P=24\text{V}$

Q. A rod $\text{AB}$ of length $0.5\text{m}$ can slide freely on a pair of smooth, horizontal rails as shown in the figure. A magnetic field $B_0$ exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the left end by a combination of a resistor and battery, as shown in the figure. The constant speed with which the rod slides after applying the external force, $F=0.5\text{N}$ must be:

1. $4{\text{ms}}^{-1}$
2. $16{\text{ms}}^{-1}$
3. $20{\text{ms}}^{-1}$
4. $8{\text{ms}}^{-1}$

Q. A wire is sliding as shown in the figure. The angle between acceleration and velocity of the wire at the instant shown is :

1. ${30}^{\circ }$
2. ${40}^{\circ }$
3. ${120}^{\circ }$
4. ${90}^{\circ }$

Q. If I place a closed loop of wire between the North and South Poles of two magnets, if I get electricity, this means I get infinite energy forever by doing nothing. How is this violation of the law of conservation of energy possible.

1. The given statement is wrong. The magnets have to be moving with respect to the coil.
2. This is an exceptional case
3. Faraday was wrong.
4. Excess energy dissipates into the air as heat.

Q. A metal rod $\text{AB}$ moves at a constant velocity $V$ in a direction perpendicular to its length. A constant uniform magnetic field $B$ 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 electric potential is highest at the centre of the rod and decrease towards its ends
2. The electric potential is lowest at the centre of the rod and increase towards its ends
3. The entire rod is at the same electric potential
4. There is an electric field in the rod

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

Q. A conducting rod $\text{AB}$ of mass $100\text{gm}$ and length $10\text{cm}$ is placed on two rails as shown. The rod carries a current of $20\text{A}$ and there is a uniform magnetic field of $1.5\text{T}$ in the surrounding space. What will be the speed of the rod as it travels through $50\text{cm}$ along the rails, if it starts from rest. Take $\mu =0.5$ between rails and rod and $g=10{\text{m/s}}^2$.

1. $0.5\text{m/s}$
2. $2.5\text{m/s}$
3. $5\text{m/s}$
4. $25\text{m/s}$

Q. If I place a closed loop of wire between the North and South Poles of two magnets, if I get electricity, this means I get infinite energy forever by doing nothing. How is this violation of the law of conservation of energy possible.

1. This is an exceptional case
2. The given statement is wrong. The magnets have to be moving with respect to the coil.
3. Faraday was wrong.
4. Excess energy dissipates into the air as heat.

Q. A vertical conducting ring of radius R falls vertically under gravity in a horizontal magnetic field of magnitude $B_0$. Direction of $B_0$ is perpendicular to the plane of ring. when speed of ring becomes $v$,

1. Points C and D are at same potential.
2. Points A and B are at same potential.
3. Time to gain speed $v$ is more than $\frac{v}{g}$
4. No current flow in ring.

Q. A vertical conducting ring of radius R falls vertically under gravity in a horizontal magnetic field of magnitude $B_0$. Direction of $B_0$ is perpendicular to the plane of ring. when speed of ring becomes $v$,

1. Points C and D are at same potential.
2. Points A and B are at same potential.
3. Time to gain speed $v$ is more than $\frac{v}{g}$
4. No current flow in ring.

Q. A square-shaped copper coil has edges of length 50 cm and contains 50 turns. It is placed perpendicular to a 1.0 T magnetic field. It is removed from the magnetic field in 0.25 s and restored in its original place in the next 0.25 s. Find the magnitude of the average emf induced in the loop during (a) its removal, (b) its restoration and (c) its motion.

Q. A metallic bob A oscillates through the space between the poles of an electromagnet (figure). The oscillations are more quickly damped when the circuit is on, as compared to the case when the circuit is off. Explain.

Q. If I place a closed loop of wire between the North and South Poles of two magnets, if I get electricity, this means I get infinite energy forever by doing nothing. How is this violation of the law of conservation of energy possible.

1. This is an exceptional case
2. The given statement is wrong. The magnets have to be moving with respect to the coil.
3. Faraday was wrong.
4. Excess energy dissipates into the air as heat.

Q. If I place a closed loop of wire between the North and South Poles of two magnets, if I get electricity, this means I get infinite energy forever by doing nothing. How is this violation of the law of conservation of energy possible.

1. This is an exceptional case
2. The given statement is wrong. The magnets have to be moving with respect to the coil.
3. Faraday was wrong.
4. Excess energy dissipates into the air as heat.

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. Point $\text{P}$ will be at higher potential and point $\text{Q}$ will be at lower potential.
4. The electric potential is lowest at the center of the rod and increase towards its ends

Q. A particle of mass $100$ g is thrown vertically upwards with a speed of $5$ m/s. The work done by the force of gravity during the time the particle goes up is :

1. 0.5 J
2. -1.25 J
3. 1.25 J
4. -0.5 J

Q. When the positively charged hanging pendulum bob is made fixed, the work done in slowly shifting a unit positive charge from infinity to $P$ is $V$. If the pendulum is free to move, the corresponding work done is $V^{{}^{\prime }}$. Then :

1. $V=V^{{}^{\prime }}$
2. $V>V^{{}^{\prime }}$
3. $V<V^{{}^{\prime }}$
4. $V\le V^{{}^{\prime }}$

Q. A vertical conducting ring of radius R falls vertically under gravity in a horizontal magnetic field of magnitude $B_0$. Direction of $B_0$ is perpendicular to the plane of ring. when speed of ring becomes $v$,

1. Points C and D are at same potential.
2. Points A and B are at same potential.
3. Time to gain speed $v$ is more than $\frac{v}{g}$
4. No current flow in ring.

Q. A vertical conducting ring of radius R falls vertically under gravity in a horizontal magnetic field of magnitude $B_0$. Direction of $B_0$ is perpendicular to the plane of ring. when speed of ring becomes $v$,

1. Points C and D are at same potential.
2. Points A and B are at same potential.
3. Time to gain speed $v$ is more than $\frac{v}{g}$
4. No current flow in ring.

Q. A vertical conducting ring of radius R falls vertically under gravity in a horizontal magnetic field of magnitude $B_0$. Direction of $B_0$ is perpendicular to the plane of ring. when speed of ring becomes $v$,

1. Points C and D are at same potential.
2. Points A and B are at same potential.
3. Time to gain speed $v$ is more than $\frac{v}{g}$
4. No current flow in ring.