The magnetic induction at the centre `O` in the figure shown in

Options

A. `(mu_(0)i)/4(1/(R_(1))-1/(R_(2)))`
B. `(mu_(0)i)/4(R_(1)+R_(2))`
C. `(mu_(0)i)/4(R_(1)+R_(2))`
D. `(mu_(0)i)/4(R_(1)+R_(2))`

Answer

A

Explanation

In the following figure magnetic field at mid point `O` due to sections `1,2,3` and `4` are considered as `B_(1), B_(2),B_(3),B_(4)` respectively.

`B_(1)=B_(3)=0`
`B_(2)=(mu_(0))/(4pi).(pii)/(R_(1)) ox`
`B_(4)=(mu_(0))/(4pi).(pii)/(R_(2)) o.` As `|B_(2)|gt|B_(4)|`
So `B_("net")=B_(2)-B_(4) implies B_("net")=(mu_(0)i)/4(1/(R_(1))-1/(R_(2))) ox`