Question

Two identical positive charges are 0.6 meters apart.
Which is true about the electric field and potential at the point which is directly in-between the two?

• A. The electric field and potential both equal zero.
• B. The electric field and potential are both positive numbers.
• C. The electric field is a positive number while the potential is a zero.
• D. The electric field is zero while the potential is a positive number.

Answer 1

Answer: (D)

The electric field is zero while the potential is a positive number.

The electric field $E$ due to a point charge $+q$ at a distance $r$ is given by ,

$E=kq/r^2$ , away from charge $+q$

as both charges are equal in magnitude and are positive therefore net electric field in between the two charges will be zero , as both fields are equal and opposite to each other .

now electric potential $V$ due to a point charge $+q$ at a distance $r$ is given by ,

$V=kq/r$

the magnitude of $V$ is taken with the sign of charge $q$ ,

electric potential $V$ due to point charge $+q$ at a distance $0.3$ (midpoint )is given by ,

$V^{\prime }=kq/0.3$

and electric potential $V$ due to another point charge $+q$ at a distance $0.3$ will be ,

$V^{\prime \prime }=kq/0.3$

therefore net potential at the center of the line joining the two like charges ,

$V=V^{\prime }+V^{\prime \prime }=2kq/0.3$