If a long horizontal conductor is bent as shown in figure and a current I is passed in it, find the magnitude and direction of magnetic field induction at the centre of circular part.

Options

A. `(mu_(0))/(4pi) (2i)/r(pi+1)`
B. `(mu_(0))/(4pi) (2i)/r(pi-1)`
C. Zero
D. Infinite

Answer

B

Explanation

The given shape is equivalent to the following diagram the field at `O` due to straight part of conductor is `B_(1)=(mu_(0))/(4pi).(2i)/r o.` . The field at `O` due to circular coil is `B_(2)=(mu_(0))/(4pi).(2pi i)/r ox`. Both fields will act in the opposite direction, hence the total field at `O`.
i.e, `B=B_(2)-B_(1)=((mu_(0))/(4pi))xx(pi-1)(2i)/r=(mu_(0))/(4pi).(2i)/r(pi-1)`