Question

Phys 162 Name January 30th, 2017 Homework 3M Potential, Gauss's Law (old friends) Due Wednesday, February 1st 1. Consider a charge of 10 nC at (1,0) cm, and of contribution from each the electric potential V at the origin. Remember that the potential to a previous problem, is a scalar. While the of this problem is identical problem is that problem asked for the electric field at the origin, not the potential. This considerably easier.

Answer 1

V_1 = q_1/4 pi epsilon_0 r_1 = 9 times 10^9 times 10 times 10^- 19 = 9 times 10^3 V V_2 = q_2/4 pi epsilon_0 r_2 = -20 times 10^- 9 times 9 times 10^9/squareroot 2 times 10^- 2 = -127.28 times 10^2 V = -12.72 times 10^3 V V = V_1 + V_2 = -3.7279 Volts outside sphere integral E dA = Q enclosed/epsilon_0 rightarrow Gauss law integral E_1 dA = theta/epsilon_0 E integral dA = Q/epsilon_0 Since E = const as Gaussian surface of roofing r. E 4 pi r^2 middot theta/epsilon_0 = > E = Q/4 pi epsilon_0 r^2 (r > R) on the surface: - integral E_1 dA = Q_enclosed/epsilon_0 = > E (4 pi R^2) = Q/epsilon_0 E = Q/4 pi epsilon_0 R^2 (r = R) Inside: integral E_1 dA = Q_enclose/epsilon_0 = > integral E dA = Q V_inside/epsilon_0 = > E integral dA = Q V)inside/V epsilon_0 E 4 pi r^2 = Q/epsilon_0