Question

You travel along a path from location A to location B, moving in a direction opposite to the direction of the net electric field in that region. What is true of the potential difference ${\mathbf{V}}_{\mathbf{B}}\mathbf{-}{\mathbf{V}}_{\mathbf{A}}\mathbf{?}\mathbf{}\mathbf{\left(}\mathbf{1}\mathbf{\right)}\mathbf{}{\mathbf{V}}_{\mathbf{B}}\mathbf{-}{\mathbf{V}}_{\mathbf{A}}\mathbf{>}\mathbf{0}\mathbf{,}\mathbf{}\mathbf{\left(}\mathbf{2}\mathbf{\right)}\mathbf{}{\mathbf{V}}_{\mathbf{B}}\mathbf{-}{\mathbf{V}}_{\mathbf{A}}\mathbf{<}\mathbf{0}\mathbf{,}\mathbf{}\mathbf{\left(}\mathbf{3}\mathbf{\right)}\mathbf{}{\mathbf{V}}_{\mathbf{B}}\mathbf{-}{\mathbf{V}}_{\mathbf{A}}\mathbf{=}\mathbf{0}\mathbf{.}$

Short answer

The correct answer for potential difference is option (1)$V_B-V_A>0$.

Step-by-step solution

Concept/Significance of the potential energy.

The work done on or by a particular charge travelling across an electrical potential difference is known as electrical potential energy.

Determination of the true potential difference.

The electric field always points from the positive charge to the negative charge, and as the electric field direction is from B to A, it is concluded that B is on the positive side and A is on the negative side. the positive side has higher potential energy than the negative side.

So, the potential difference is negative when potential of point A is placed first which is given by,

$∆V=V_A-V_B$and,

The potential difference is positive when potential of point B is placed first which is given by,

$∆V=V_B-V_A$

Thus, the correct answer for potential difference is option (1)$V_B-V_A>0$.