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a charge is uniformly distributed on a circular ring of radius r now the ring is rotated with angular velocity w about the diameter of the ring. calculate the magnetic moment of the circular ring
Hiii I am calculating the magnetic moment of the circular ring at the centre of the ring.The total magnetic induction at the centre of the ring will be mew* q*w/4*pie*rI = q/tI = q*w/2*pieMagnetic field at the centre of current carrying conductor = mew*I / 2*rPutting the value of I we ger B = mew* q*w/4*pie*r
The total magnetic induction at the center of the ring will be μ₀qω/4πrExplanation:since the total charge is q and we know that current = charge/time=> I = q/tThe angular velocity is equal to ω = 2π/tTime period, t = 2π/ω=> I = qω/2πwe know that magnetic field at the center of a current carrying conductor,B = μ₀I/2rputting the value of I from the above equation, we getB = (μ₀/2r) x qω/2π=> B = μ₀qω/4πrHence the total magnetic induction at the center of the ring will be μ₀qω/4πr
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