A current `I` flows an infinitely long wire with cross section in the form of a semi - circular ring of radius `R`. The magnitude of the magnetic induction along its axis is :

Options

A. `(mu_(0)I)/(2 pi^(2)R)`
B. `(mu_(0)I)/(2 pi R)`
C. `(mu_(0)I)/(4 pi^(2)R)`
D. `(mu_(0)I)/(pi^(2)R)`

Answer

B

Explanation

Let us select one Amperian loop of radius R and total current will be enclosed in it. We can write the following equation:
`B xx 2 pi R = mu_(0)I`
` rArr " " B = (mu_(0)I)/(2 pi R) `
Hence , option (b) is correct.