Question

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

• A. $\frac{\mu_0 I}{\pi r}$
• B. $\frac{\mu_0 I}{2\pi r}$
• C. 0
• D. $\frac{2\mu_0 I}{\pi r}$

Hint:

For two parallel currents in the same direction, fields at the midpoint cancel.

Answer 1

The Correct Option is C

To determine the magnetic field intensity at the midpoint between two parallel wires carrying current in the same direction, we can use Ampère's Law and the Biot-Savart Law.

Consider two long, straight, parallel wires separated by a distance of \(2r\), each carrying a current \(I\) in the same direction. Let's analyze the magnetic field at point P, which is midway between the two wires (at a distance \(r\) from each wire).

1. According to the right-hand rule, the magnetic field due to the first wire (\(B_1\)) at point P is directed into the plane (since current flows upwards), and its magnitude is calculated using the formula: \(B_1 = \frac{\mu_0 I}{2\pi r}\)
2. The magnetic field due to the second wire (\(B_2\)) at point P is directed out of the plane (as it also carries current in the same direction), and its magnitude is also: \(B_2 = \frac{\mu_0 I}{2\pi r}\)
3. Due to their opposite directions, \(B_1\) and \(B_2\) will cancel each other out at point P: \(B = B_1 - B_2 = \frac{\mu_0 I}{2\pi r} - \frac{\mu_0 I}{2\pi r} = 0\)

Thus, the intensity of the magnetic field at the midpoint between the wires is zero. Hence, the correct answer is \(0\).