An infinite hollow cylinder of radius R with uniform surface charge density σ rotates with angular speed ω. If the magnetic field at its centre is B=μ₀σRω·x, find x.
Physics · Magnetic effect of current
JEE Mains

Question

An infinite hollow cylinder of radius R with uniform surface charge density σ rotates with angular speed ω. If the magnetic field at its centre is B=μ₀σRω·x, find x.

G1 Physics · Accepted Answer

A rotating charged cylindrical shell is equivalent to surface current density K=σv=σωR. The field inside an infinite current sheet/cylinder is B=μ₀K=μ₀σωR. Hence x=1.