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Two short magnets P and Q are placed one...

Two short magnets P and Q are placed one over another with their magnetic axes mutually perpendicular to each other. It is found that resultant magnetic field at a point on the prolongation of magnetic axis of P is inclined at `30^@` with this axis. Compare the magnetic moments of the two magnets.

Text Solution

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In figure, at any point A, distant r from the centre of two magnets.
magnetic field due to P, `B_1=(mu_0)/(4pi)(2M_1)/(r^3)`
magnetic field due to Q, `B_2=(mu_0)/(4pi)(M_2)/(r^3)`.

As resultant field is inclined at `30^@` with `B_1`, therefore, `tan beta=B_2/B_1=(M_2)/(2M_1)=tan30^@=1/sqrt3`
`:. M_1/M_2=sqrt3/2`
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