At the vertices of a square with a side of 0.5 m there are charges of the same size.

At the vertices of a square with a side of 0.5 m there are charges of the same size. In the case when two adjacent charges are positive and the other two are negative, the field strength in the center of the square is 144 V / m. determine the charge.

The field in the center of the square is determined by the superposition of two fields created by pairs of charges located on the diagonal E1 and E2, since the charges are the same, the fields will also be the same. Since the diagonals of the square are perpendicular, by the Pythagorean theorem the equality is true:

E ^ 2 + E ^ 2 = 144 ^ 2;

2E ^ 2 = 144 ^ 2;

E ^ 2 = 36 ^ 2;

E = 36.

The field strength of a point charge is determined by the formula:

E = q / 4πε0.

Since there are two charges, we get:

q = E / 8πε0 (ε0 = 8.85 * 10 ^ (- 12).

q = 36/8 * π * 8.85 * 10 ^ (- 12) = 0.16 * 10 ^ (12).