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

Answer

1

Explanation

`v=1/(piR)`
`dB=((mu_(0))/(4pi))(2I)/R I=lambdaR d theta`
`:.B=underset(-pi//2)overset(pi//2)intdBcos theta=(mu_(0)lambda)/(2pi)underset(-pi//2)overset(pi//2)int cos theta d theta=(mu_(0)lambda)/pi=(mu_(0)I)/(pi^(2)R)`