A small sphere of char go q = + 69 mu C and nun m = 5.6 g is attached to a light

Question

A small sphere of char go q = + 69 mu C and nun m = 5.6 g is attached to a light string and placed in a uniform electric field E^rightarrow that makes an angle theta = 35 degree with the horizontal. The opposite end of the string is attached to a wall and the sphere is in static equilibrium when the string is horizontal as in the figure shown below Construct a free body diagram for the sphere. (Submit a file with a maximum size of 1 MB.) Find the magnitude of the electric field Find the tension in the string (Enter the magnitude of the tension in the string.)

Explanation / Answer

E = ?
m = 5.6 g = 5.6 * 10^-3 kg
q = 69 uC

Electric Force in vertical direction, F = q*E*sin(35)
We know the sphere is in equilibrium So it the electric force should balance the weight !!
q*E*sin(35) = m*g
Substituing Values,
69 * 10^-6 * E * sin(35) = 5.6 * 10^-3 * 9.8
E = 1386.7 N/C

(c)
Equating the Horizontal forces,
Tension in the string , T = qE * cos(35)
T = 69 * 10^-6 * 1386.7 * cos(35)
T = 0.0783 N

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