A metal disc of radius a rotates with a constant angular velocity `omega` about its axis. The potential difference between the center and the rim of the disc is `("m = mass of electron, e = charge on electro")`

Options

A. `(momega^(2)a^(2))/(e)`
B. `(1)/(2)(momega^(2)a^(2))/(e)`
C. `(eomega^(2)a^(2))/(2m)`
D. `(eomega^(2)a^(2))/(m)`

Answer

B

Explanation

Let `E` be the elecric field at a distance `r` from the centre of disc. Then
`eE=momega ^(2)r`
or `E=(momega^(2)r)/(e)`
:. `P.D.=int_(r=0)^(r=0)E dr`
`=int_(0)^(a)(momega^(2)r)/(e)=(momega^(2)a^(2))/(2e)`