Two Parallel Currents

Q.

Two very long straight parallel wires carry currents of same magnitude and in the same direction. 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 $\overrightarrow{v}$ is perpendicular to this plane. The magnitude of the force due to magnetic field acting on the charge at this instant is

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

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

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

4. $Zero$

Q. A high resistance galvanometer is connected to two identical 1.5V cells . when the cells are in series the galvanometer reads 1.0 amp, and when the cells are in parallel it reads 0.6 amp .find the internal resistance of each cell.

Q. Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a 25 cm length of wire C is

1. ${10}^{-3}$ N
2. $2.5\times {10}^{-3}$ N
3. Zero
4. $1.5\times {10}^{-3}$ N

Q.

Two very long straight parallel wires carry currents of same magnitude and in the same direction. 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 $\overrightarrow{v}$ is perpendicular to this plane. The magnitude of the force due to magnetic field acting on the charge at this instant is

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

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

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

4. $Zero$

Q.

A long horizontally fixed wire carries a current of 100A. Directly above and parallel to it is another wire carrying a current of 20 A and weighing 0.04 N m^-1 . What should be the separation between the two wires so that the upper wire is just supported by magnetic repulsion?

1. 1 cm

2. 2 cm

3. 3 cm

4. 4 cm

Q. Two long thin wires ABC and DEF are arranged as shown in the figure. They carry equal currents I. The magnitude of the magnetic field at O is

1. Zero
2. $\frac{{\mu }_{0}I}{4\pi a}$
3. $\frac{{\mu }_{0}I}{2\pi a}$
4. $\frac{{\mu }_{0}I}{2\sqrt{2}\pi a}$

Q. Two parallel wires carry currents of $20\text{A}$ and $40\text{A}$ in opposite directions. Another wire carrying a current antiparallel to $20\text{A}$ is placed midway between the two wires. The magnetic force on it will be

1. Towards $20\text{A}$
2. Towards $40\text{A}$
3. Zero
4. Perpendicular to the plane of the current

Q. A toroid of $N$ turns, mean radius $r$ and cross- sectional radius $a$ is connected across a battery of emf $V$. If the magnetic field inside the core of toroid is $B$, find the value of $V$. Take resistance per unit length of wire equal to $\rho$.
[wires are closely wounded on toroid]

1. $\frac{2{\pi }^{2}Nra\rho B}{{\mu }_{0}N}$
2. $\frac{2\pi Nra\rho B}{{\mu }_{0}N}$
3. $\frac{4{\pi }^{2}Nra\rho B}{{\mu }_{0}N}$
4. $\frac{2{\pi }^{3}Nra\rho B}{{\mu }_{0}N}$

Q. An arrangement of three infinitely long straight wires placed perpendicular to plane of paper carrying same current $I$ along the same direction is shown in the figure. The magnitude of force per unit length on wire $\text{B}$ is