A disk of radius R rotates with constant angular velocity ω about its own axis. Surface charge density of this disc varies as σ = α r 2 where 'r' is the distance from centre of disc. Determi

Question

A disk of radius R rotates with constant angular velocity ω about its own axis. Surface charge density of this disc varies as σ = α r 2 where 'r' is the distance from centre of disc. Determine the magnetic field intensity at the centre of disc.

TestHub · Accepted Answer

d q = σ ( 2 π r d r ) = 2 π α r 3 d r ; d i = d q 2 π ω ​ = α ω r 3 d r d B = 2 r μ 0 ​ d i ​ = 2 μ 0 ​ α ω r 2 ​ d r B = 2 μ 0 ​ α ω ​ ∫ 0 R ​ r 2 d r = 6 μ 0 ​ α ω R 3 ​ Hence (B).

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