We have three forces acting on the ball: mg, string tension, and electric force.
The electric force must be repelling the ball away from the wall. We'll represent these forces in a free body diagram then decompose any 2D forces into their x and y components. Finally, We'll apply Newton's second law in the x and y-directions.
Newton's second law:
2D vector components:
where θ is the angle measured from the x-axis.
A small 12.8 g plastic ball is tied to a very light 25.2 cm string that is attached to the vertical wall of a room. (See the figure.) A uniform horizontal electric field exists in this room. When the ball has been given an excess charge of -1.20 μC, you observe that it remains suspended, with the string making an angle of 17.4° with the wall.
a) Find the magnitude of the electric field in the room.
b) Find the direction of the electric field in the room.
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