Question

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 42 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? show work please

Answer 1

The electric force between two point charges at a distance r can be given by EF=kq1q2/(rxr)

In this question, we firstly calculate the individual electric force due to each charge and then find the direction of the resultant force. We find that if when the charge at origin is q, the angle made from +x axis is 42°(as given in the question.

From the figure, we can imply that the net Ef along x axis is in the +x direction and y axis is in the +y direction which gives us this resultant direction.

Now from the corresponding tan theta if we change the charge by q'=-4.1q, we can say the electric force by individual charges will start acting in the opposite direction, which will hence give us a new tan theta.

we find that the resultant Electric force comes out to be in the third quadrant accordingly as in the given figure.

Therefore, new angle = 222° counter clockwise from +x axis.