1.

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 isA. 3BB. `sqrt(5)B`C. `(sqrt(5))/(2)B`D. `B`

Answer» Correct Answer - B
Since , for magnet P, axis lies along X-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 equatorial line w.r.t. magnet Q.
Hence , magnetic field due to magnet Q,
`B_(Q)=(mu_(0))/(4pi)(M)/(x^(3))=B" "`[R `implies` equatorial point ] .......... (i)
Magnetic field due to magnet P,
`B_(P)=(mu_(0))/(4pi)(2M)/(x^(3))=2B" "`[R= axial point ] .......... (ii)
As at point R magnetic field due to P and Q magnet are perpendicular to each other ,
`B_(R) implies` Net magnetic field at R due to magnet P and is given as Q,
`B_(R)implies sqrt(B_(P)^(2)+B_(Q)^2)=sqrt(B^(2)+(2B)^(2))=sqrt(5)B`


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