Consider the circular loop having current i and with central poin… - Vidyadip

MCQ

Consider the circular loop having current $i$ and with central point $O$. The magnetic field at the central point $O$ is

A
$\frac{2 \mu_0 i }{3 \pi R }$ acting downward
✓
$\frac{5 \mu_0 i }{12 R }$ acting downward
C
$\frac{6 \mu_0 i }{11 R }$ acting downward
D
$\frac{3 \mu_0 i }{7 R }$ acting upward

✓

Answer

Correct option: B.

$\frac{5 \mu_0 i }{12 R }$ acting downward

b
(b)

Magnetic field at the center due to the inner loop of radius $R=\frac{3}{4} \times \frac{\mu_0 I}{2 R}$ downwards

Magnetic field at the center due to the outer loop of radius $3 R=\frac{1}{4} \times \frac{\mu_0 I}{2(3 R)}$ downwards

Magnetic field at center due to the two straight wire segments is zero.

Hence net magnetic field at center of loop $=\frac{3 \mu_0 I}{8 R}+\frac{\mu_0 I}{24 R}$ downwards $=\frac{5 \mu_0 I}{12 R}$ downwards

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