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Two solenoids acting as short bar magnet...

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 magnitude is

A

3B

B

`sqrtB`

C

`(sqrt5)/(2)B`

D

B

Text Solution

Verified by Experts

Since for magnet P, axis lies alonX-axis and for magnet Q, axis is along Y-axis. The point R is along axial line w.r.t. magnet P, and is along equalorital line w.r.t. magnet Q.
Magnet field due to magnet Q
`B_(Q)=(mu_(0))/(4pi) (M)/(x^(3))=B "[" "R Rightarrow equatorial point" "]"`
magnetic field due to magnet P
`B_(P)=(mu_(0))/(4pi) (2M)/(x^(3))=B "[" "R=axial point" "]"`
As at a point R magnetic field due to P and Q magnet are perpendicular to each other, ,
`B_(R) Rightarrow` Net magnetic field due to magnet P and is given as Q. `B_(R) Rightarrow sqrt(B_(p)^(2)+B_(Q)^(2))=sqrt(B^(2)+(2B)^(2))=sqrt5B`
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