Question

Suppose you have a fixed charge of -15.0 nC at point X. Points A and B are at distances of 20.0 cm and 40.0 cm from X as shown. 15.0 nC Calculate the following: a. the potential at points A and B b. the potential difference between A and B c. the potential energy of a proton at A and B d. the speed at point B of a proton that was moving to the right at point A with a speed of 4.0 x 105 m/s the speed at point A of a proton that was moving to the left at point B with a speed of 1.0 x 105 m/s e.

Answer 1

Potential at point A, V_A = q/4pi E_0 (X A) = -15 times 10^-9 times 9 times 10^9/(20 times 10^-2) = -15 times 9/2 times 10^-1 [assuming 1/4pi E_0 = 9 times 10^9 N - m^2/c^2 = -15 times 9/2 times 10^-1 = -675V (Ans)/potential at point B, V_B = q/4 pi E_0(x B) = -15 times 10^-9 times 9 times 10^9/40 times 10^-2 = -337.5 V (Ans) potential difference between points A & B, V_AB = (V_A - V_B) = [(-675) - (-337.5)] = -337.5V \r\n charge of a proton, q = + 1.6 times 10^19 C potential energy of a proton at A, W_A = qV_A = [1.6 times 10^-19 times (-675)] = (-1.08 times 10^-16) J(Ans) potential energy of proton at B, W_B = qV_B = [1.6 times 10^-19 times (337.5)] = (-5.4 times 10^-17) J (Ans) speed of the proton at A, V_A = 4 times 10^5 m/s kinetic energy of the proton at A, F_k_A = 1/2 mV_A^2