Two Parallel Currents

Q.

The force of repulsion between two parallel wires is $f$ when each one of them carries a certain current $I$. If the current in each is doubled, the force between them would be,

1. $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$f$}\right.$

2. $4f$

3. $2f$

4. $f$

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 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. Two long straight wires are set parallel to each other. Each carries a current i in the same direction and the separation between them is 2r. The intensity of the magnetic field midway between them is

1. $\frac{{\mu }_{0}i}{r}$
2. $\frac{4{\mu }_{0}i}{r}$
3. Zero
4. $\frac{{\mu }_{0}i}{4r}$

Q. Two very long, straight, and insulated wires are kept at $90°$ angle from each other in $x-y$ plane as shown in figure.


These wires carry currents of equal magnitude $I$, whose directions are shown in the figure. The net magnetic field at point $\text{P}$ will be:

1. $\frac{{\mu }_{0}I}{2\pi d}(\hat{x}+\hat{y})$
2. $-\frac{{\mu }_{0}I}{2\pi d}(\hat{x}+\hat{y})$
3. $\frac{+{\mu }_{0}I}{\pi d}\left(\hat{z}\right)$
4. Zero

Q. Two very long, straight, and insulated wires are kept at $90°$ angle from each other in $x-y$ plane as shown in figure.


These wires carry currents of equal magnitude $I$, whose directions are shown in the figure. The net magnetic field at point $\text{P}$ will be:

1. Zero
2. $\frac{{\mu }_{0}I}{2\pi d}(\hat{x}+\hat{y})$
3. $-\frac{{\mu }_{0}I}{2\pi d}(\hat{x}+\hat{y})$
4. $\frac{+{\mu }_{0}I}{\pi d}\left(\hat{z}\right)$

Q. A long wire A carries a current of 10 amp. Another long wire B, which is parallel to A and separated by 0.1 m from A, carries a current of 5 amp in the opposite direction to that in A. What is the magnitude and nature of the force experienced per unit length of B
$[{\mu }_0=4\pi \times {10}^{-7}weber/amp-m]$

1. Repulsive force of ${10}^{-4}N/m$
   
2. Attractive force of ${10}^{-4}N/m$
   
3. Repulsive force of $2\pi \times {10}^{-5}N/m$
   
4. Attractive force of $2\pi \times {10}^{-5}N/m$

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. $\frac{{\mu }_{0}I}{2\sqrt{2}\pi a}$