Two positive and two negative point particles, all with charge of magnitude (j =

Question

Two positive and two negative point particles, all with charge of magnitude (j = 5nC, are placed at the 4 aimers of a 10 cm-side square as shown. Determine the electric field, magnitude and direction, at the center of the square. Determine the energy required to assemble these four point charges from far apart to the presen configuration. An electron (m, = 9.11 x 1(>31 kg) is placed at the center of the square with zero initial velocity. Determine its instantaneous acceleration, both direction and magnitude, due to the four point charges at the corners.

Explanation / Answer

a) Clearly the direction will be positive y, since the positive charges pushes it towards y and the negative charges attract it towards y. Magnitude = E = [4* k * q / r^2 ] * cos 45 Here r = a / sqrt(2) = 7.07 cm So, E = [4 * 9 *10^9 * 5*10^-9 * 1/sqrt(2)] / 50 = 2.545 N/C b) U = Ke ((q1q2/r12) + (q1q3/r13) + (q1q4/r14) + (q2q3/r23) + (q2q4/r24) + (q3q4/r34)) r12, r23, r34, r14 = 10 cm r24, r13 = 14.14 cm U = Ke ((5 * -5/.1) + (5 * 5/.1414) + (5 * -5/.1) + (-5 * 5/0.1) + (-5 * -5/.141) + (5 * -5/.1)) U = Ke ((4X (-24/.1)) + (2X (25/.1414)) U = Ke * -606.39 * 10^-18 U =-5.457 MJ c) Force on electron = E*q = 2.545 * 1.6 * 10^-19 = 4.07 * 10^ -19 N m = 9.1 10^-31 kg So, a = F / m = 4.475 * 10^11 m/s^2

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