Question

Four point charges have the same magnitude of 3.6x 10-12 c and are fixed to the corners of a square that is 5.9 cm on a side. Three of the charges are positive and one is negative. Determine the magnitude of the net electric field that exists at the center of the square. Number Units the tolerance is +/-3%

Answer 1

Charge q = 3.6 * 10^-12 C

side of the square a = 5.9 cm = 0.059 m

Diagonal = sqrt(2) * a = 0.0834 m

distance of the center from corner r = diagonal / 2 = 0.04171 m

electric field due to two positive charges which are lies on same diagonal are equal in magnitude but opposite in direction.So, they cancel each other.

Therefore net electric field E = E ' + E "

where E ' = electric field due to charge +q

E' = Kq/r² = 9*10⁹*3.6*10^-12/(0.04171 )²

E' = 18.62 N/C

E " = electric field due to charge -q

E'' = Kq/r² = 9*10⁹*3.6*10^-12/(0.04171 )²

E'' = 18.62 N/C

E ' and E " are in same direction.

So,

E =37.24 N / C