A cylindrical capacitor with external radius R, internal radius `R-d(dltltR )`, length l and mass M hangs on an insulating cord in a region where there is a homogenous, vertical magnetic field of strength B. It can rotate freely as a whole around its vertical axis, but is constrained, so that it can not move horizontally.

Charge on capacitor is given by

Options

A. `in_(0)(2piRlV)/(d)`
B. `in_(0)(piRlV)/(2d)`
C. `in_(0)(piRlV)/(3d)`
D. `in_(0)(piRlV)/(4d)`

Answer

A

Explanation

`d ltlt R`
`therefore C=in_(0)(2piRl)/(d)`
`Q=CV=(in_(0)2pirlV)/(d)`
`MR^(2) (domega)/(dt)=IBRd=BRd(dQ)/(dt)`
`impliesMR^(2) Deltaomega = BRdDeltaQ`
`impliesomega_(max)=(2piin_(0)VBl)/(M)`