Question

Calculate the magnitude of the electric field at the center of a square with sides 20.5 cm long if the corners, taken in rotation, have charges of 1.18 μC, 2.36 μC, 3.54 μC, and 4.72 μC (all positive).

Answer 1

given,

magnitude of the charges at the four corners of the square = 1.8 uC, 2.36 uC, 3.54 uC, 4.72 uC

side of the square = 0.205 m

so,

distance of the center of the square to the corners = side of the square / sqrt(2)

distance of the center of the square to the corners r = 0.205 / sqrt(2)

distance of the center of the square to the corners r = 0.145 m

charges 1.18 uC and 3.54 uC will be opposite to each other so their electric field will be opposite to each other, same case with charge 2.36 uC and 4.72 uC

electric field = kQ / r^2

electric field due to 1.18 uC and 3.54 uC charge = (k/r^2)(3.54 * 10^-6 - 1.18 * 10^-6)

electric field due to 1.18 uC and 3.54 uC charge = (9 * 10^9 /0.145^2) (3.54 * 10^-6 - 1.18 * 10^-6)

electric field due to 1.18 uC and 3.54 uC charge = 1.01 * 10^6 N/C

electric field due to 2.36 uC and 4.72 uC charge = (k/r^2) (4.72 * 10^-6 - 2.36 * 10^-6)

electric field due to 2.36 uC and 4.72 uC charge = (9 * 10^9 /0.145^2) (4.72 * 10^-6 - 2.36 * 10^-6)

electric field due to 2.36 uC and 4.72 uC charge = 1.01 * 10^6 N/C

since the angle between two fields is 90 degree

net electric field = sqrt(2) * 1.01 * 10^6

the magnitude of the electric field at the center of a square = 1.428 * 10^6 N/C