A current carrying wire is bent as shown in the figure. Find magnetic field at centre 'O' of the semi-circles. (take R1 = 4π and R2 = 6π)

Question

A current carrying wire is bent as shown in the figure. Find magnetic field at centre 'O' of the semi-circles. (take \(R_1 = 4\pi\) and\(R_2 = 6 \pi\))

(1) \(8.3I \times 10^{-6} T\)

(2) \(8.3I \times 10^{-9}T\)

(3) \(4 \pi I \times 10^{-7} T\)

(4) \(6I \times 10^{-8} T\)

Answer 1

Correct option is:  (2) \(8.3I \times 10^{-9}T\)

\(B = \frac{\mu_0 I}{4 R_1} - \frac{\mu_0 I}{4R_2}\)

\(= \frac{4 \pi \times 10^{-7} I}{4} \left( \frac{1}{4\pi} - \frac{1}{6 \pi} \right)\)

\(= \frac{1}{12} \times 10^{-7} I\)

\(= 8.3 I \times 10^{-9} T\)