Two circular coils `P` and `Q` are made from similar wire but radius of `Q` is twice that of `P`. Relation between the values of potential difference across them so that the magnetic induction at their centers may be the same is

Options

A. `V_(q)-2V_(p)`
B. `V_(q)=3V_(p)`
C. `V_(q)=4V_(p)`
D. `V_(q)=1/4V_(p)`

Answer

C

Explanation

`B_(1)=(mu_(0))/(4pi)[(2piI_(1))/(r_(1))]and B_(2)=(mu_(0))/(4pi)[(2pil_(2))/(r_(2))]`
Since, `B_(1)=B_(2)and r_(2)=2r_(1), I_(2)=2I_(1)`
`therefore (V_(2))/(V_(1))=(I_(2)R_(2))/(I_(1)R_(1))=(2I_(1))/(I_(1))xx(2R_(1))/(R_(1))=4/1`