Force on a Current Element

Q. Two large conducting plates of a parallel plate capacitor are given charges $Q$ and $3Q$ respectively. If the electric field in the region between the plates is $E_o$ , then the force of interaction between the plates is :

1. $\frac{3Q{E}_o}{2}$
2. $3Q{E}_o$
3. $\frac{2Q{E}_o}{3}$
4. $\frac{Q{E}_o}{2}$

Q. When a wire is subjected to a force of 100 N, then length of wire is 1.05 m. Again wire is subjected to a force of 200 N, Then length of wire is 1.15 m, the natural length of wire is

Q. spring of force cons†an t k is cut into lengths of ratio1:2:3. they are connectd in series and new force con†an t is k. and connected in parallel and force cons†an t is k". then k/k

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

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 stretching force
3. A compressive force
4. A torque

Q. Two wires A and B are made of same material. The wire A has a length l and diameter r while the wire B has a length 2l and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is
(a) 1/8
(b) 1/4
(c) 4
(d) 8

Q. A straight wire carrying a current $i_1$ runs along the axis of a circular current $i_2$. Then the force of interaction between the two current carrying conductors is

1. $\infty$
2. Zero
3. $\frac{{\mu }_0}{4\pi }\frac{2i_1{i}_2}{r}$
4. $\frac{2i_1{i}_2}{r}\frac{N}{m}$

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

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

Q. An equilateral triangular coil of 10 turns carrying 1A current is placed in uniform magnetic field of 4T as shown in figure. If side of triangle is 1m then torque acting on coil is