Force on a Current Element

Q. An elastic circular wire of length l carries a current I. It is placed in a uniform magnetic field $\overrightarrow{B}$ (Out of paper) such that its plane is perpendicular to the direction of $\overrightarrow{B}$. The wire will experience

1. No force
2. A torque
3. A stretching force
4. A compressive force

Q. A long, thin-walled pipe of radius R carries a current I along its length. The current density is uniform over the circumference of the pipe. The magnetic field at the centre of the pipe due to quarter portion of the pipe is

1. None
2. $\frac{{\mu }_{0}I\sqrt{2}}{4{\pi }^{2}R}$
3. $\frac{{\mu }_{0}I}{{\pi }^{2}R}$
4. $\frac{2{\mu }_{0}I\sqrt{2}}{{\pi }^{2}R}$

Q. A particle with charge q and mass m is projected with kinetic energy K into the region between two plates of a uniform magnetic field B as shown below.

If the particle is to miss collision with the opposite plate, the maximum value of B is

1. $\frac{\sqrt{2Kq}}{md}$
2. $\frac{\sqrt{2K}}{qmd}$
3. $\frac{\sqrt{2Kd}}{qm}$
4. $\frac{\sqrt{2Km}}{qd}$

Q.

A conducting circular loop of radius r carries a constant current i. It is placed in a uniform magnetic field , such that is perpendicular to the plane of the loop. The magnetic force acting on the loop is?

[BIT 1992; MP PET 1994; IIT 1983;MP PMT 1999; AMU (Engg.) 2000]

1. 
   

2. Zero

3. 
   

4. 
   

Q. Two long wires are hanging freely. They are joined first in parallel and then in series and then are connected with a battery. In both cases, which type of force acts between the two wires

1. Repulsion force in both cases
2. Attraction force when in parallel and repulsion force when in series
3. Repulsion force when in parallel and attraction force when in series
4. Attraction force in both cases

Q. A metallic block carrying current I is subjected to a uniform magnetic field $\overrightarrow{B}$ as shown in the figure. The moving charges experience a force $\overrightarrow{F}$ given by ........... which results in the lowering of the potential of the face ........ Assume the speed of the carriers to be v

1. $eVB\hat{k},ABCD$
2. $-eVB\hat{k},ABCD$
3. $-eVB\hat{k},EFGH$
4. $eVB\hat{k},EFGH$

Q. Two very long, straight and parallel wires carry steady currents I and I respectively. The distance between the wires is d. At a certain instant of time, a point charge q is at a point equidistant from the two wires in the plane of the wires. Its instantaneous velocity v is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is

1. $0$
2. $\frac{{\mu }_{0}Iqv}{2\pi d}$
3. $\frac{{\mu }_{0}Iqv}{\pi d}$
   
4. $\frac{2{\mu }_{0}Iqv}{\pi d}$
   

Q. In the figure, AB is a long straight wire carrying a current of 20A and CDFG is a rectangular loop of size 20 cm x 9cm carrying a current of 10A. The edge CG is parallel to AB, at a distance of 1cm from it. The force exerted on the loop by the magnetic field of the wire is

1. $3.6\times {10}^{-4}N$ attraction
2. $3.6\times {10}^{-4}N$ epulsion
3. $7.2\times {10}^{-4}N$ attraction
4. $7.2\times {10}^{-4}N$ repulsion

Q. A rod of mass m and length L is kept on two connection points a and b in a uniform magnetic field B. As soon as switch S is closed rod jumps to height H. Charge flown through the battery is

1. $\frac{m}{LB}2\sqrt{2gH}$
2. $\frac{m}{3LB}\sqrt{gH}$
3. $\frac{m}{LB}\sqrt{2gH}$
4. $\frac{m}{LB}\sqrt{gH}$

Q. A conducting wire is sliding in a uniform magnetic field. As the wire moves, emf is induced, and according to Lenz's law, motion is retarded. The work done by the magnetic field is given by $W_{magnetic}$. Then,

1. $W_{magnetic}$ is positive since electrons are being pumped for current flow.
2. $W_{magnetic}$ is negative, since motion is being retarded.
3. None of the above.
4. $W_{magnetic}$ is zero, became magnetic force is always $\perp$ to velocity.