There is a parallel plate capacitor with charge of magnitude Q = 0.5 mC on each

Question

There is a parallel plate capacitor with charge of magnitude Q = 0.5 mC on each plate. Each plate has an area A = 0.015 m^2.

Hanging from a string made of insulating material is an object with a mass m = 2g. The string makes an angle of 10 degrees with the vertical. The string is attached at the top to an insulating material with negligible dielectric properties.

A) What are the magnitude and direction of the field inside the capacitor?

B) What is the charge of the object?

C) If the string is cut, what would be the acceleration of the object?

Explanation / Answer

A) E = Q/A*eo = 0.5e-6/(0.015*8.84e-12) = 3.77e6 N/C

B) along vertical Fg = mg = T*cos10

along horiZantal Fe = Eq = T*sin10

tan 10 = Eq/mg

tan 10 = (3.77e6*q)/(2e-3*9.8)

q = 0.916 *10^-9 C

C)

a_g = g

a_E = E*q/m = (3.77e6*0.916e-9)/(2e-3) = 1.726

a = sqrt(a_g^2 +a_E^2)

a = 9.95 m/s^2

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