Question

Please help with this problem please thank you

Physics 221 General Physics Π-Calculus Supplement Spring 2019 Homework I #1. Calculate the magnitude of the electric field acting at a location a distance D away from the end of a thin wire of length I carrying a total charge Q, as shown below Express your answer in terms of D, Q. L, and other constants. E=? 2

Answer 1

Charge density (lambda) = Q/L Consider a charge element dx at a distance x from the D Now charge on dx, dq = lambda dx field due to charge element at D is. integral dE vector = integral 1/4 pi epsilon_0 times dq/x^2 integral dE = 1/4 pi epsilon_0 integral_D^D + L lambda dx/x^2 = lambda/4 pi epsilon_0 [-1/x]_D^D + L E = -lambda/4 pi epsilon_0 [1/D + L - 1/D] = -lambda/4 pi epsilon_0 [D - D - L/D(D + L)] = lambda L/4 pi epsilon_0 D (D + L) Therefore magnitude of electric field is lambda L/4 pi epsilon_0 D(D + L)