A) A small styrofoam ball of mass M with charge Q is suspeneded in the air (does

Question

A) A small styrofoam ball of mass M with charge Q is suspeneded in the air (doesnt fall due the gravity ) a distance Y above yhr center of a horizontal charged ring with charge QR and radius R. What is the charge on the ring.



B) Consider the same ball and ring experiment from problem 4. In this case, the charge on the ring is Qr (Not the value you found in problem 4 ) but the radius of the ring and charge on the ball are the same as above. What would be the work done by the electric force between the ball and the ring if the ball is moved from the point Yi above the center of to the center of the ring ?

A small styrofoam ball of mass M with charge Q is suspeneded in the air (doesnt fall due the gravity ) a distance Y above yhr center of a horizontal charged ring with charge QR and radius R. What is the charge on the ring. Consider the same ball and ring experiment from problem 4. In this case, the charge on the ring is Qr (Not the value you found in problem 4 ) but the radius of the ring and charge on the ball are the same as above. What would be the work done by the electric force between the ball and the ring if the ball is moved from the point Yi above the center of to the center of the ring?

Explanation / Answer

A) electric field due to ring

E = k*Q*Y/(R^2+Y^2)^3/2

in the equilibrium

Electric force = gravitational force

QR*E = M*g

QR*(k*Q*Y/(R^2+Y^2)^3/2 ) = M*g


==> Q = M*g*(R^2+Y^2)^1.5/(QR*k*Y)

B)


Electric potential due to a chrged ring on its axis

Vi = k*QR/sqrt(R^2+Y^2)

= 9*10^9*1.6*10^-6/(sqrt(0.21^2*0.34^2)

= 3600 volts

Electric potential due to a chrged ring at its center

Vf = k*QR/R

= 9*10^9*1.6*10^-6/0.21

= 68571 volts

workdone by electic force, W = Q*(Vi-Vf)

= 5.4*10^-9*(3600-68571)

= -3.5*10^-4 J

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