Two wires wrapped over a conical frame from the coils `1` and `2`. If they produce no net magnetic field at the apex `P`, the value of

Options

A. `sqrt((r_(2))/(r_(1)))`
B. `(r_(2))/(r_(1))`
C. `((r_(1))/(r_(2)))^(2)`
D. `sqrt((r_(1))/(r_(2)))`

Answer

B

Explanation

`B=(mu_(0))/(4pi) (2M)/(x^(3))=(mu_(0))/(4pi) (ipir^(2))/((r//sin theta)^(3))`
`implies B prop i/r B_(1) =B_(2) implies (i_(1))/(r_(1))=(i_(2))/(r_(2)) implies (i_(1))/(i_(2))=(r_(1))/(r_(2))`