A non-conducting spherical shell of radius 50 mm has uniform surface charge density 10.0 μC/m² and rotates at 70 rad/s about a diameter. Find the magnetic induction at the centre in pT.
Physics · Magnetic effect of current
JEE Advanced

Question

A non-conducting spherical shell of radius 50 mm has uniform surface charge density 10.0 μC/m² and rotates at 70 rad/s about a diameter. Find the magnetic induction at the centre in pT.

G1 Physics · Accepted Answer

A uniformly charged rotating spherical shell has magnetic moment μ=(QωR²)/3 and its centre field is B=2μ₀μ/(4πR³)=μ₀Qω/(6πR). With Q=4πR²σ, B=(2/3)μ₀σωR. Substitution gives about 29 pT.