Question

The magnitude of magnetic induction at mid point 'O' due to current arrangement as shown in figure will be (\(μ_0\) = permeability of free space)

• A. \(\frac{μ_0I}{2πa}\)
• B. zero
• C. \(\frac{μ_0I}{4πa}\)
• D. \(\frac{μ_0I}{πa}\)

Hint:

Only the two vertical semi-infinite wires matter at O; the horizontal wires point toward O.

Answer 1

The Correct Option is D

Step 1: Use the formula
For a wire ending at the foot of the perpendicular, $B = \frac{\mu_0I}{4\pi d}$ with $d = \frac a2$.

Step 2: Add
Both contributions point the same way, so $B = 2\cdot\frac{\mu_0I}{2\pi a} = \frac{\mu_0I}{\pi a}$. Option (D).

Final Answer:
mu0 I / (pi a). \[ \boxed{\text{(D)}\ \frac{\mu_0I}{\pi a}} \]