A small ball with mass m =1.0g hangs on an insulating massless string of length

Question

A small ball with mass m=1.0g hangs on an insulating massless string of length 55 cm. The ball is placed in a uniform horizontal electric field with magnitude 1.85×104 N/C , In equilibrium, the ball is deflected as shown, such that it lies 12 cm above its lowest (vertical) position.

Part A

What is the magnitude of the charge on the ball?

Q = _______________C

Part B

If the directions of the field and displacement are as shown in the figure, what is the sign of the charge on the ball? Positive or negative?

Explanation / Answer

here ,

L = 55 cm

for h = 12 cm

h = L * (1 - cos(theta))

12 = 55 *(1 - cos(theta))

theta = 38.6 degree

Now, for equilibrium of the ball ,

m*g = T * cos(theta)

q * E = T * sin(theta)

>>>

tan(theta) * mg = q * E

q = tan(38.6) * 0.001 * 9.8/1.85 *10^4

q = 4.22 *10^-7 C

the charge on the ball is 4.22 *10^-7 C

part B)

as electric force is in the direction of field ,

the charge on the ball is POSITIVE

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