A small 0400 g sphere carries a charge of 30010 C and is att

A small 0.400 g sphere carries a charge of 3.00^-10 C and is attached to one end of a silk fiber 8.00 cm long the other end of the fiber is attached to a large vertical insulating sheet that has surface charge density equal to 25.0*10^-6 C/m^2. The sphere on the end of the fiber is repelled outward and finally reaches a state of equilibrium. Find the angle that the fiber makes with the vertical sheet.

Solution

Here ,

electric field due to large sheet , E = charge density/(2 * epsilion_0)

E = 25 *10^-6/(2 * 8.854 *10^-12)

E = 1.412 *10^6 N/C

electric force on the charge , F = q * E

F = 1.412 *10^6 * 3 *10^-10 N

F = 4.235 *10^-4 N

Now , let the angle is theta

for the angle

tan(theta) = F/(m * g)

tan(theta) = 4.235 *10^-4 /(0.4 *10^-3 * 9.8)

theta = 6.2 degree

the angle of fibre with the sheet is 6.2 degree