Question

An infinitely long straight conductor is bent into the shape as shown below. It carries a current of $I$ ampere and the radius of the circular loop is $R$ metre. Then, the magnitude of magnetic induction at the centre of the circular loop is -

• A. $\frac{\mu _0I}{2 \pi R}$
• B. $\frac{\mu _nI}{2 R}$
• C. $\frac{\mu _0I}{2 \pi R} \pi + 1$
• D. $\frac{\mu _0I}{2 \pi R } \pi -1$

Answer 1

Answer: (C)

$\frac{\mu _0I}{2 \pi R} \pi + 1$

Answer 2

Magnetic field due to long wire at $O$ point
$B_1 = \frac{\mu_0}{2\pi} \frac{I}{R}$ upward direciton
Magnetic field due to loop at $O$ point
$B_2 = \frac{\mu_0}{4\pi} . \frac{I.2 \pi R}{R^2}$
$B_2 = \frac{\mu_0}{2} . \frac{I}{R}$ in upward direction
Hence, resultant magnetic field at centre $O$
$B = B_1 + B_2$
$B = \frac{\mu_0 I}{2 \pi . R} \pi + T$