A uniformly charged rod of length 2 m and total charge 4 C rotates with angular speed 6 rad/s about an axis through its centre perpendicular to the rod. Find the magnetic dipole moment in A·m².
Physics · Magnetic effect of current
JEE Advanced

Question

A uniformly charged rod of length 2 m and total charge 4 C rotates with angular speed 6 rad/s about an axis through its centre perpendicular to the rod. Find the magnetic dipole moment in A·m².

G1 Physics · Accepted Answer

For charge element dq=(q/ℓ)dx at distance |x|, dμ=(ω/2)x²dq. Integrating from −ℓ/2 to +ℓ/2 gives μ=qωℓ²/24. With q=4 C, ω=6 and ℓ=2 m, μ=4 A·m².