In a bent wire shown in figure, a current `I` is passed. Find the value of `B` at the common centre.

Options

A. `(mu_(0)I(b-a)(2pi-theta))/(4piab)`
B. `(mu_(0)la(2pi-theta))/(4pib)`
C. `(mu_(0)lb(2pi-theta))/(4pia)`
D. `(mu_(0)labtheta)/(4pi)`

Answer

A

Explanation

The sraight segments make no contribution to the field at the centre . By Biot-Savart's law the field at the centre due to curved segments is

`DeltaB=(mu_(0)1)/(4pi)[(a(2pi- theta))/(a^(2))-(b(2 pi- theta))/(b^(2))]`
`=(mu_(0)1)/(4pi)(2pi- theta)[1/a-1/b]=(mu_(0)I(2pi-theta)(b-a))/(4piab)`