Question

+4 +Q a. Find the electric Field vector E at point P (0, +a). (Calculate the magnitude, and draw b. c. d. the vector in the picture.) Sketch the electric field lines. Find the electric Field E at (x, 0) for x >a Find out the location (x, y) where the electric Field E becomes zero. (Hint: Use the solution of e).

Answer 1

a) E_1 = K 4Q/(squareroot 2a)^2 = 2 kQ^2/a^2 E_2 = kQ/(squareroot 2 a)^2 = kQ/2a^2 E_net = (E_1 sin 30 - E_2 sin 30) i^^+ (E_1 + E_2) cos 0 j^^= (KQ/q^2 - kQ/4q^2) i^^+ 5/2 times squareroot 3/2 kQ/q^2 j^^= 3/4 kQ/a^2 i^^+ 5 squareroot 3/4 kQ/q^2 j^^ Vertical-bar E_net Vertical-bar = squareroot (3/4 kQ/2)^2 + (5 squareroot 3/4 kQ/q^2)^2 = 2.29 kQ/a^2 \r\n c) E = k Q/(x - a)^2 + 4 kQ/(x + 2a)^2 d) E = 0 kQ/(x - 9)^2 = -4 kQ/(x + 2q)^2 (x + 2q)^2 = -4 (x - 9)^2 x^2 + 4q^2 + 4qx = -4x^2 - 4q^2 + 8qx 5x^2 - 4qx + 8q^2 = 0 x = 4q plusminus squareroot 16a62 - 160 q^2/10