Question

Four particles, each of charge $+q$, are arranged symmetrically on the $x-$axis about the origin as shown. A fifth particle of charge $-Q$ is placed on the positive $y-$axis as shown. What is the direction of the net electrostatic force on the charge $-Q$?

• A. $\uparrow$ positive $y-$ axis
• B. $\to$ positive $x-$ axis
• C. $\downarrow$ negative $y-$ axis
• D. $\leftarrow$ negative $x-$ axis

Answer 1

The correct option is C $\downarrow$ negative $y-$ axis

The negative charge is attracted to each of the positive charges.
The components of the attractive force along the $x-$axis from the inner two positive charges are by symmetry of equal magnitude and in opposite directions. Hence, they cancel out each other. The same argument applies to the forces due to the outer two positive charges.
So, net force on $-Q$ along $x-$axis is zero.
The components of the attractive force along the $y-$axis from all positive charge on negative charge gets added up.
Therefore, the total force on $-Q$ is along negative $y-$axis.