Question

Please see the question below, please double check all numbers and unit conversions and double check your answer. Thank you!!

Below the question is a guide of how to work some of the question out.

A charge is located at the origin, another charge is located somewhere on the +y axis, another charge is located somewhere on the -y axis, and a fourth is located somewhere on the +x axis. The angle of the total electric force on the charge at the origin is 32 degrees counter-clockwise from the +x axis. Then, the charge at the origin changes sign and its magnitude (absolute value of its charge) increases by a factor of 4.1. All other charges do not move or change their signs or magnitudes. What is the angle of the total electric force on the charge at the origin now measured in degrees counter-clockwise from the +x axis?

Answer 1

Ans

The change in the magnitude of the charge at origin doesn't have any effect on the direction of the electric force on the charge at the origin. The magnitude of the charge appears in both x and y component of the total electric force on it. So when we find the direction using tan identity, the magnitude of the charge cancels out.

Due to the change in sign of the charge, the direction of the total electric increases by180(the total electric force vector reflects about the origin). So the direction of the total electric force with the + x in counterclockwise direction = 32 + 180 = 212 degrees.

The electric force is shown by Fnew in the figure below.