Question

Three identical bar magnets, each of pole strength $ 10\;Am\; $ and length $ 10\,cm $ are placed in a uniform field of induction $ 0.05\;Wb/{m^2} $ . If the three magnets are fastened end to end along the same axis with opposite poles touching each other, the resulting magnetic moment in $ A{m^2} $ is:
A) 3
B) 9
C) 6
D) 8

Answer 1

Hint When the three bar magnets are attached together, their length will increase but the pole strength will remain constant. The magnetic moment Is calculated as the product of the pole strength with the length of the bar magnets.

Formula used: In this solution we will be using the following formula,
 $\Rightarrow M = mL $ where $ M $ is the magnetic moment of a magnet for which, $ m $ is the pole strength and $ L $ is the length of the bar magnet.

Complete step by step answer
The magnetic moment of a magnet characterizes how strong its tendency to get aligned to an external magnetic field is. We’ve been given that three bar magnets are placed in an external field such that their ends are fastened together with the opposite poles touching each other.
Since the length of the other magnet is $ 10\,cm $ , So the total length of the combination will be
 $\Rightarrow 3 \times 0.1 $
 $\Rightarrow 0.3\,m $
The magnetic moment can thus be calculated as the product of the pole strength and the length of the bar magnets as
 $\Rightarrow M = mL $
Since all the 3 bar magnets have the same pole strength, the magnet formed from the combination will have the same pole strength as the 3 individual bar magnets. So, substituting the value of $ m = 10Am $ and $ L = 0.3\,m $ , we can calculate the magnetic moment as
 $\Rightarrow M = 10 \times 0.3 $
 $ \therefore M = 3 $ which corresponds to option (A).

Note
The magnetic moment of any magnet is dependent on its dimensions and is independent of the external magnetic field so the external magnetic field provided in the question is irrelevant. The direction of the magnets when they are fastened end to end must be carefully chosen since magnetic moments are vectors and if any two magnets were aligned with the same poles touching each other, they would cancel out their magnetic moments.