Question

3- Electric force Consider the setup illustrated beside which shows two identical balls with a mass of 25 g each, attached with strings of identical length to a support. Both balls are charged positively so they repel each other. The one on the left is only charged with 0.1 uC but the one on the right with 100 uC. The angle between the two strings sets at 90 degrees. A) What is the horizontal distance between the two charged balls? .B) What is the strings length?

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Answer 1

(A) From F.B.D: T cos 45 degree = mg (1) T sin 45 = F (2) From (1): T cos 45 degree = mg T/squareroot 2 = (25 times 10^-3) times 9.8 T = squareroot 2 (25 times 10^-3) times 9.8 N T = 0.346 N From (2): 0.346 times 1/squareroot 2 = F_e 0.24466 = F_e 0.245 = 9 times 10^9 times (0.1) (100) times 10^-12/r^2 r^2 = 9 times 10^9 times (0.1) (100) times 10^-12/0.245 r^2 = 0.367 r = 0.606 m rightarrow Horizontal distance between the two charges. \r\n (B) By Geometry: cos 45 degree = r/2/l l = r/2 cos 45 degree = 0.606/2 times 1/squareroot 2 l = 0.606/squareroot 2 l = 0.429 m rightarrow length of string.