A mad scientist is designing a trap for intruders that will liftthem up into the

Question

A mad scientist is designing a trap for intruders that will liftthem up into the air and hold them helpless. The device consists ofan equilateral triangle, 10.0 meters to a side, embedded in hisfloor. When he flips a switch, the corners of the triangle will becharged equally by a generator and any negatively charged objectabove the center of the triangle will be lifted upwards by theelectric force. A computer-controlled system of giant fans keepsthe intruder from straying horizontally from the center of thetriangle. While he is testing the system, his cat walks into thetrap. She has a net charge of 1.00 nanocoulombs due toelectrons that rubbed off from the carpet. The cat, which has amass of 5.00 kg, begins to hover 3.00 meters up in the air.Find the charge on each corner of the triangle.

Explanation / Answer

a = 10.0 m, q = 1.00 nC, m = 5.00 kg, h = 3.00 m, find Q the distance between the center and any charge Q is d =a/3 note the resultant electric force on the cat must be upward, tobalance the gravity, so Q and q must have same sign, Q is alsonegative. the distance between the cat and any Q is r, r2 =h2 + d2 = h2 + a2/3 net electric force on the cat = 3*kqQ/r2 cos =3*kqQ/r2 *h/r = 3kqQh/r3 =3kqQh/(h2 + a2/3)3/2 = mg Q = mg(h2 + a2/3)3/2/(3kqh)= 167 C answer: -167 C

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