Q.Calculate the magnetic field at a point on the axial line of a bar magnet.

Step 1. For a bar magnet NS (length $2l$, pole strength $q_m$), place a unit north pole at point $C$ on the extended axis, distance $r$ from the centre $O$.

Step 2. Field due to N (distance $r-l$): $B_N=\dfrac{\mu_0}{4\pi}\dfrac{q_m}{(r-l)^2}$, pointing away from N. Field due to S (distance $r+l$): $B_S=\dfrac{\mu_0}{4\pi}\dfrac{q_m}{(r+l)^2}$, pointing toward S. Since $C$ is nearer N, $B_N>B_S$, and the net field points from S to N. …

Superpose the two individual pole fields along the axis, then apply the sh …

• Forgetting to apply the short-magnet approximation, leaving an unwieldy exact expre …