A small 6.3g plastic ball is suspended by a 28cm long string in a uniform electric field of 4400N/C in the +x direction. If the ball is in equilibrium when the string makes a 25.9 angle with the vertical, what is the net charge on the ball?© BrainMass Inc. brainmass.com October 5, 2022, 5:15 pm ad1c9bdddf
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Assume that the tension on the rope is T.
Since the ball is at equilibrium, the net force on the ball is zero.
Hence, the net vertical force = 0 and the net horizontal force = 0
Vertical Direction: There are two forces on the y direction.
1. A component of the tension force T cos θ
2. Weight mg
Net force in the vertical direction is T cos θ - mg
T cos θ - mg = 0
T = mg/cos θ = 0.0063 *9.8/cos 25.9 = 0.069 N
T = 0.069 N
Horizontal Direction: There are two forces on the x direction.
3. A component of the tension force T sin θ
4. The electric force Eq = 4400 x q
Net horizontal force on the ball is T sin θ - 4400 q
T sin θ - 4400 q = 0
Solving for q,
q = T sin θ /4400 = 0.069 * sin 25.9 /4400 = 6.85 x 10-6 C
q = 6.85 μC