Question

You travel along a path from location A to location B, moving in a direction perpendicular to the direction of the net electric field in that region.

What is true of the potential difference ${\mathbf{V}}_{\mathbf{B}}\mathbf{-}{\mathbf{V}}_{\mathbf{A}}$?

$$\begin{gathered} \left(1\right)\mathbf{}\mathbf{}{\mathbf{V}}_{\mathbf{B}}\mathbf{-}{\mathbf{V}}_{\mathbf{A}}\mathbf{>}\mathbf{0}\mathbf{,} \\ \left(2\right)\mathbf{}\mathbf{}{\mathbf{V}}_{\mathbf{B}}\mathbf{-}{\mathbf{V}}_{\mathbf{A}}\mathbf{<}\mathbf{0} \\ \left(3\right)\mathbf{}\mathbf{}{\mathbf{V}}_{\mathbf{B}}\mathbf{-}{\mathbf{V}}_{\mathbf{A}}\mathbf{=}\mathbf{0} \end{gathered}$$

Short answer

${\mathrm{V}}_{\mathrm{B}}-{\mathrm{V}}_{\mathrm{A}}<0$,is the correct option.

Step-by-step solution

Potential difference.

The difference of electrical potential between two points.

$\mathrm{V}=\mathrm{IR}$

Solution.

You travel along a path from location A to location B, moving in a direction perpendicular to the direction of the net electric field in that region,. Here the diagram define this statement more clearly,

Electric field from $\mathrm{A}\mathrm{to}\mathrm{B}$.

${\mathrm{V}}_{\mathrm{B}}-{\mathrm{V}}_{\mathrm{A}}=\left(-\mathrm{Ve}\right)$because, It goes to electric field always goes higher potential to lower potential. but, ${\mathrm{V}}_{\mathrm{B}}\mathrm{to}{\mathrm{V}}_{\mathrm{A}}$is the opposite direction.

Hence option “b” ,${\mathrm{V}}_{\mathrm{B}}-{\mathrm{V}}_{\mathrm{A}}<0$, is the correct option.