Two charges lie on the x axis, +2q at the origin, and −3q at x = 5.0 m. The point on the x axis where the electric potential has a zero value (when the value at infinity is also zero) is
A) 1.0 m.
B) 2.0 m.
C) 2.5 m.
D) 3.0 m.
E) 4.0 m.

Question

Quizplus · Accepted Answer

The electric potential $V$ at a point due to a point charge $q$ at a distance $r$ is given by $V = kq/r$, where $k$ is Coulomb's constant. The total potential at a point due to multiple charges is the algebraic sum of the potentials due to each charge. For the potential to be zero, the potential due to the +2q charge must equal in magnitude but opposite in sign to the potential due to the -3q charge. Let $x$ be the distance from the +2q charge to the point where the potential is zero. Then, the distance from the -3q charge to this point is $5 - x$. Setting the magnitudes of the potentials equal and opposite gives $k(2q)/x = k(3q)/(5-x)$. Solving for $x$ gives $x = 2.0$ m.

Two Charges Lie on the X Axis, +2q at the Origin