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

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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 by Roar3215 ~Expert~ (1,298 points)
    

1 Answer

+5 votes
 
Best answer
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 pokemonmaster ~Expert~ (3,842 points)
selected Jan 28, 2012 by Roar3215

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