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A long cylinder with uniformly charged s...

A long cylinder with uniformly charged surface and crosssectional radius `a = 1.0 cm` moves with a constant velocity `v = 10 m//s` along its axis. An electric field strength at the surface of the cylinder is equal to `E = 0.9 kV/cm`. Find the resultign concection current , that is, the current caused by mechanical transfer of a charge.

Text Solution

Verified by Experts

The conservection current is
`I = (dq)/(dt)` ....(1)
here, `dq = lambda dx`, wehre `lambda` is the linear charge density.
But, from the Gauss' theorem, electric field at the surface of the cylinder,`E = (lambda)/(2pi epsilon_(0) a)`
Hence, substituting the value of `lambda` and subsequenty of `dq` in Eqs. (1), we get
`I = (2E pi epsilon_(0) adx)/(dt)`
`= 2pi epsilon_(0) E av`, as `(dx)/(dt) = v`
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