# If the thread makes an angle θ with the vertical, what is the potential difference between the plates?

A small object of mass m carries a charge q and is suspended by a thread between the vertical plates of a parallel-plate capacitor. The plate separation is d. If the thread makes an angle θ with the vertical, what is the potential difference between the plates? (Use any variable or symbol stated above along with the following as necessary: g.)

ΔV =

asked Jan 27, 2012 in Physics

First establish all the forces action on the object.

Fy = forces acting on y component

Fx = forces acting on x component

Fy = 0:  and so, T*cos(theta) - m*g = 0   (T = tension of thread, m=mass, g=gravity)

Fx = 0:  and so, T*sin(theta) - E*q = 0  (E=electric field, q=charge)

Combine the 2 equations by dividing Fx by Fy, resulting in:

tan(theta) = (E*q) / (m*g)

now solve for E.

E = tan(theta)*(m*g) / q

The formula for potential difference V, is:

V = E*d

so substitute E from above into this equation and you get that:

V =  (tan(theta)*(m*g*d)) / q
answered Jan 28, 2012 by ~Expert~ (3,839 points)
selected Jan 28, 2012 by Roar3215