The resistance of wire `ABC` is double of resistance of wire `ADC`. The magnetic field at `O` is

Options

A. `(mu_(0)i)/(12R), o.`
B. `(mu_(0)i)/(6R), o.`
C. `(mu_(0)i)/(3R), o.`
D. `(mu_(0)i)/(2R), o.`

Answer

A

Explanation

`R_(1)=2R_(0),R_(2)=R_(0)`
`i_(1)=(R_(2))/(R_(1)+R_(2))xxi=i/3, i_(2)=i-i_(1)=(2i)/3`
`B_(1)=(mu_(0)i_(1))/(4R)=(mu_(0)i)/(12R), ox`
`B_(2)=(mu_(0)i_(2))/(4R)=(mu_(0)i)/(6R), o.`
`B_(O)=B_(2)-B_(1)=(mu_(0)i)/(12R), o.`