A non-conducting thin disc of radius R charged uniformly over one side with surface density σ rotates about its axis with an angular velocity ω . Find:
Text Solution
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Sol. We consider a ring element of radius r and thickness dr.
The area of considered element is dA = 2 π rdr
∴ The electric charge on the considered element is
dq = σ dA = 2 πσ rdr
∴ The convection current due to considered element is
dI = 
= 
= σω rdr
∴ The magnetic field at the centre due to considered element is
dB = 
= 
∴ The magnetic field due to disc is
∴ B = 
∴ B = 
σω R
The magnetic moment due to considered ring is
dP m = π r 2 dI = π r 2 σω rdr = πσω r 3 dr
∴ P m = πσω 
∴ P m = πσω 
= 
.
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