Question

Please only round for the final answer

A metal sphere hangs from a string and has 4 kg of mass. The sphere has a charge of +2.7 μC, A uniform electric field is turned on and directed to the righ (a) Which way does the sphere move? left right (b) What is the electric force on the metal sphere if the magnitude of the electric field is 10 N/C? (c) When the sphere reaches equilibrium, what is the angle that the string makes with the vertical axis (assuming the same electric field as part (b))?

Answer 1

Mass of metal sphere = 4 kg Charge on sphere = 2.7 mu C (a) Here electric field is from Left to Right. So, the sphere (positive charge) moves to the Right. (b) Now electric field = 10^6 N/C Sp, F = qE = (2.7 times 10^-6 C) (10^6 N/C) F = 2.7 N (c) Now, Solve for the sum of forces along x, and equate to zero since they are in equilibrium. \r\n F_x = F - T cos theta = 0 2.7 = T cos theta rightarrow (1) Now F_y = T sin theta - w = 0 T sin theta = w T sin theta = mg rightwardsdoublearrow 4 times 9.8 T sin theta = 39.2 rightarrow (1) divide eq^n (2) by eq^n (1), we get tan theta = 39.2/2.7 theta = tan^-1 (14.5185185) theta = 86.06 degree (w.r.t. x-axis) Now with vertical theta = 90 - 86.06 theta = 3.94 degree