Question

Two very long, straight, and insulated wires are kept at a 90° angle from each other in the x-y plane as shown in the figure. These wires carry equal currents of magnitude \( I \), whose directions are shown in the figure. The net magnetic field at point P will be:

• A. \( \frac{\mu I}{2\pi (x + y)} \)
• B. \( -\frac{\mu I}{2\pi (x + y)} \)
• C. \( \frac{\mu I}{\pi (x + y)} \)
• D. Zero

Hint:

For magnetic fields created by current-carrying wires at a point, use the superposition principle to find the net magnetic field by adding the fields vectorially. If the fields are of equal magnitude and opposite in direction, they may cancel each other out.

Answer 1

The Correct Option is D

Given that there are two straight wires carrying current \( I \) at a 90° angle, the magnetic field at point \( P \) will be the vector sum of the magnetic fields due to each of the wires. The magnetic field at a point due to a straight current-carrying wire is given by: \[ B = \frac{\mu I}{2 \pi r} \] where \( r \) is the distance from the wire to the point of interest. For each wire, the magnetic field will have different directions, but since the currents are of equal magnitude and the angle between the wires is 90°, the fields from both wires will cancel each other out at point \( P \). Therefore, the net magnetic field at point \( P \) is: \[ B_{\text{net}} = 0 \] Thus, the net magnetic field at point P is zero.