Question

PLEASE PROVIDE SOLUTION IN VECTOR FORM AND SHOW ALL STEPS. THANK YOU!

A plastic rod 1.8 m long is rubbed all over with wool, and acquires a charge of -3e-08 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A0.7, 0, 0 > m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece. 6 j zero magnitude (a) What is the length of one of these pieces? e0.225 (b) What is the location of the center of piece number 4? 0, 0.1125, 0)m (c) How much charge is on piece number 4? (Remember that the charge is negative.) 3.75e-9 coulombs (d) Approximating piece 4 as a point charge, what is the electric field at location A due only to piece 4? E44629.26, - 1487.98,0N/C (e) To get the net electric field at location A, we would need to calculate E due each of the 8 pieces, and add up these contributions. If we did that, which arrow above would best represent the direction of the net electric field at location A?

Answer 1

Charge on the piece 4 is q = -3.75 times 10^-9 c length of piece 4 is l = 0.225 m. Now we draw only piece 4. l/2 = 0.225/2 = 0.1125 distance of point charge q from point A is r = squareroot (0.1125)^2 + (0.7)^2 r = 0.7089 m. from coulombs law electric field at point A due to the point charge q. E = q/4 pi epsilon_0 r^2\r\n E = 9 times 10^9 times 3.75 times 10^-9/(0.7089)^2 therefore 1/4 pi epsilon_0 = 9 times 10^9 E = 33.75/0.5025 E = 67.164 N/c Now we draw this field at point A cos theta = 0.7/0.7089 = 0.987 sin theta = 0.1125/0.7089 sin theta = 0.158 x-component of electric field is E_x = -E cos theta = -67.164 times 0.987 E_x = -66.290 N/c y-component of electric field is E_y = E sin theta = 6.164 times 0.158 =\r\n