Question

1. hree charges and an infinitely lng charged line are placed as shown below, where -q -1.6x10 C,- 4.0x10 C/m, and 8-30 93 42 a. Ifd 2cm is the distance from qu to the origin, what distance D must the line charge λ be placed from the origin in order to ensure that there is no net electric force on gi? b. Ifcharges 2 and 3 were moved further from the x-axis, would the necessary value of D increase, decrease, or stay the same? Answer this conceptually, without any calculations.

Answer 1

a Electric field due to an infinitely long line charge at a distance x from the line where charge density in lambda is given by lambda/2 pi epsilon_0 x here the distance of q_1 from the line charge is d + D. Therefore E_L = lambda/2 pi epsilon_0 (d + D) \r\n The field q_1 due to q_3 E_q_3 = 1/4 pi epsilon_0 q_3/r^2 where r is the distance between q_1 & q_3 r = d/cos theta rightwardsdoublearrow E_q_3 = 1/4 pi epsilon_0 q_3 cos^2 theta/d^2 Similarly E_q_2 = 1/4 pi epsilon_0 q_2 cos^2 theta/d^2 For q_1 to have no electric force on it E_q_2 sin theta = E_q_3 sin theta This is the case as q_2 = q_3. & E_q_2 cos theta + E_q_3 cos theta = E_L rightwardsdoublearrow 1/4 pi epsilon_0 q_2 cos^3 theta/d^2 + 1/4 pi epsilon-0 q_3 cos^3 theta/d^2 = lambda/2 pi epsilon_0 (d + D) \r\n q_2 = q_3 rightwardsdoublearrow 2 times 1/4 pi epsilon_0 q_2 cos^3 theta/d^2 = lambda/2 pi epsilon_0 (d + D)