Question

Four point charges are placed at the corners of a square with diagonal 2a as shown. What is the total electric field at the center of the square?

• A. kq/a${}^2$ at an angle 45${}^o$ above the +x-axis
• B. kq/a${}^2$ at an angle 45${}^o$ below the - x-axis
• C. 3kq/a${}^2$ at an angle 45${}^o$ above the - x-axis
• D. 3kq/a${}^2$ at an angle 45${}^o$ below the +x -axis

Answer 1

The correct option is B kq/a${}^2$ at an angle 45${}^o$ below the - x-axis

At center electric due to both 3q will be canceled because electric field due to that is equal and in opposite direction. Now net field at center is
$E=E_1-E_2$
$=\frac{k2q}{(a{)}^2}-\frac{kq}{(a{)}^2}=\frac{kq}{(a{)}^2}$
This is 45${}^o$ below negative x-axis.