A current carrying wire AB of the length L is turned along a circle, as shown in figure. The magnetic field at the centre O.

Options

A. `(mu_(0)pii)/(L)((2pi-theta)/(3pi))`
B. `(mu_(0)pii)/(L)((2pi-theta)/(2pi))`
C. `(mu_(0)pii)/(L)(2pi-theta)`
D. `(mu_(0)pii)/(L)(2pi+theta)^(2)`

Answer

A

Explanation

Let r be the radius of new are AB
`therefore r(2pi-theta)=L` or `r=(L)/((2pi-theta))`
`therefore` Manetic field at centre O is
`B=(mu_(0)i)/(2r)((2pi-theta)/(2pi))=(mu_(0)pii)/(L)((2pi-theta)/(2pi))^(2)`