An inclined plane of inclination `theta` is placed in uniform horizontal electric field `E` as shown. A block of mass `m` having charge `q` is sliding down on the plane with constant velocity . If coefficient of friction is `mu` , find charge `q` in terms of given quantities .

Explanation

The forces acting on the block are as shown.
Since block is moving with constant velocity , the net force on it zero .
`_|_^(ar)` to the plane : `N = mg cos theta + qE sin theta`
Along the plane : `mg sin theta = qE cos theta + f = qE cos theta + mu N`
`= qE cos theta + mu(mg cos theta + qE sin theta)`
`qE(cos theta + mu sin theta) = mg(sin theta - mu cos theta)`
`q = (mg (sin theta - mu cos theta))/(E (cos theta + mu sin theta)) = (mg)/(E ) ((tan theta - mu))/((1 + mu tan theta))`