Question

In a circular loop of radius \( R \), current \( I \) enters at point \( A \) and exits at point \( B \), as shown in the figure. The value of the magnetic field at the centre \( O \) of the loop is:

• A. \( \dfrac{\mu_0 I}{R} \)
• B. zero
• C. \( \dfrac{\mu_0 I}{2R} \)
• D. \( \dfrac{\mu_0 I}{4R} \)

Hint:

If current enters and exits a full circular loop at two diametrically opposite points, the current splits into two semicircles. The magnetic field at the center due to each half cancels the other if they carry equal current in opposite directions.

Answer 1

The Correct Option is B

Let’s consider the situation carefully. The loop shown is a complete circular loop, but the current enters at point A and exits at point B, splitting equally into two symmetrical semicircular paths (upper and lower halves of the circle). This means the current in both the upper and lower semicircles flows in opposite directions around the loop. Each semicircular arc contributes a magnetic field at the center \( O \) with equal magnitude but in opposite directions. \[ B_{\text{semicircle}} = \frac{\mu_0 I}{4R} \] So: - The upper semicircle contributes a field \( B \) into the page (say). - The lower semicircle contributes a field \( B \) out of the page. Since the magnitudes are equal and directions are opposite: \[ B_{\text{net}} = \frac{\mu_0 I}{4R} - \frac{\mu_0 I}{4R} = 0 \] % Final Answer Statement Answer: \( \boxed{\text{(B)} \ \text{zero}} \)