A thin magnet of original magnetic moment M is bent sharply at its midpoint. After bending, the magnetic-moment vectors associated with the two equal halves make an angle 2α with each other. Pole strength and the magnetic moment magnitude of each half remain unchanged.
The magnitude of the resultant magnetic moment is:

Question

A thin magnet of original magnetic moment M is bent sharply at its midpoint. After bending, the magnetic-moment vectors associated with the two equal halves make an angle 2α with each other. Pole strength and the magnetic moment magnitude of each half remain unchanged.

The magnitude of the resultant magnetic moment is:

G1 Physics · Accepted Answer

Each half has magnetic moment magnitude M/2. The angle between the two half-moment vectors is 2α. Therefore, by vector addition, M' = √[(M/2)²+(M/2)²+2(M/2)²cos2α]. Using 1+cos2α = 2cos²α, M' = (M/2)√[2+2cos2α] = (M/2)√(4cos²α) = M cosα for 0≤α≤90°. Hence option B is correct.