Two solenoids acting as short bar magnets P and Q are arranged such that centers 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, mid-way between their centers, if B is the magnitude of induction due to Q, then the magnitude of total induction at R due to the both magnets is
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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,
… (i)
Magnetic field due to magnet P,
… (ii)
As, at point R, magnetic field due to P and Q magnet are perpendicular to each other and 
net magnetic field at R due to magnet P and Q. i.e.
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