Question

4. Point P is located at the center of the square below. Draw a vector with its tail on point P indicating the direction of the electric field at the point. If the value of the electric field at P due to one point charge is E, what is the value due to the 4 point charges for each case? Show work. +Q +Q O P O P -Q +Q -Q -Q

Answer 1

E_1 = E_3 and opposite in Direction so they cancel each other Similarly E_2 and E_4 are cancel each other. Therefore net electric field at p is zero E_1 and E_3 are equal in magnitude and direction. So resultant of E_1 and E_3 is E prime = E_1 and E_3 = E + E = 2 E Similarly E_2 and E_4, resultant E Prime = E_2 + E_4 = 2 E E prime and E Prime are perpendicular to each other Therefore net field E_r = squareroot (E prime)^2 + (E Prime)^2 E_r = squareroot (2E)^2 + (2E)^2 = squareroot 4E^2 + 4E^2 = squareroot 8E^2 = squareroot 8 E Direction: downward