Two wires are wrapped over wooden cylinder to form two co-axial loops carrying currents `i_(1)` and `i_(2)`. If `i_(2)=8i_(1)` the value of `x` for `B=0` at the origin `O` is:

Options

A. `(sqrt(7)-1)R`
B. `sqrt(5) R`
C. `sqrt(3) R`
D. `sqrt(7) R`

Answer

D

Explanation

`B_(1)=B_(2) implies (mu_(0))/(4pi) (2i_(1)piR^(2))/((R^(2)+R^(2))^(3//2))=(mu_(0))/(4pi) (2i_(2)piR^(2))/((x^(2)+R^(2))^(3//2))`
given `i_(2)=8i_(1)`
Solve to get `x=sqrt(7)R`