Two solenoids acting as short bar magnets P and Q are arranged such that their centres are on the X-axis and are separated by a large distance . The magnetic axes of P and Q are along X and Y-axes, respectively. At a point R, midway between their centres , if B is the magnitude of induction due to Q , then the magnitude of total induction at R due to the both magnets is

Options

A. 3B
B. `sqrt5B`
C. `(sqrt5)/(2)B`
D. B

Answer

b

Explanation

(b)
`B_(R)=sqrt(B_(p)^(2)+B_(Q)^(2))=sqrt(((mu_(0))/(4pi)(2M)/(d^(3)))^(2)+((mu_(0))/(4pi)(M)/(d^(3)))^(2))`
`=sqrt5(mu_(0))/(4pi)(M)/(d^(3))=sqrt5B, {B_(Q)=(mu_(0))/(4pi)(M)/(d^(3))=B}`