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tsl199 - Current within ring dI = dQ T = σ(2 πrdr ω 2 π...

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Magnetic Moment of a Rotating Disk Consider a nonconducting disk of radius R with a uniform surface charge density σ . The disk rotates with angular velocity . Calculation of the magnetic moment : Total charge on ring: Q = σ ( πR 2 ) . Divide the disk into concentric rings of width dr . Period of rotation: T = 2 π ω .
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Unformatted text preview: Current within ring: dI = dQ T = σ (2 πrdr ) ω 2 π = σωrdr. • Magnetic moment of ring: dμ = dI ( πr 2 ) = πσωr 3 dr . • Magnetic moment of disk: μ = Z R πσωr 3 dr = π 4 σR 4 ω. • Vector relation: ~μ = π 4 σR 4 ~ω = 1 4 QR 2 ~ω. tsl199 – p.1/1...
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