Question

Two long straight parallel wires are separated by a distance of \(20\) cm. Each wire carries current \(5\) mA in the same direction. The magnetic field at a point P midway between them is \(\{\mu _{0}=\) permeability of free space\(\}\)

• A. \(0.05\mu _{0}\) Wb/m\({}^{2}\)
• B. \((0.05/8)\mu _{0}\) Wb/m\({}^{2}\)
• C. \((0.05/4)\mu _{0}\) Wb/m\({}^{2}\)
• D. zero.

Hint:

At the midpoint the two fields are equal in magnitude but opposite in direction.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Each wire gives a field \(B=\dfrac{\mu_0I}{2\pi r}\) at distance \(r=10\) cm from it.

Step 2: Directions
Currents are in the same direction, so the fields at the midpoint are opposite (one into the page, one out of it).

Step 3: Net field
The magnitudes are equal because the currents and distances are equal, so \(B_{net}=B-B=0\).

Final Answer:
The net magnetic field at the midpoint is zero. \[ \boxed{\text{(D) }\text{zero}} \]