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Question

(A) We know that the electric field $\overrightarrow{E}$ is related to the electric potential $\phi$ by the relation $\overrightarrow{E} = -
abla \ph

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Planes parallel to the $yz$-plane

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(A) We know that the electric field $\overrightarrow{E}$ is related to the electric potential $\phi$ by the relation $\overrightarrow{E} = -
abla \phi$.The equipotential surface is defined as a surface where the potential $\phi$ is constant,which implies that the electric field $\overrightarrow{E}$ must be perpendicular to the surface at every point.Since the electric field is directed along the $x$-axis,the surfaces perpendicular to this field must lie in the plane formed by the other two axes,which are the $y$ and $z$ axes.Therefore,the equipotential surfaces are planes parallel to the $yz$-plane.

For an electric field that increases in magnitude along the $x$-direction,what is the nature of the equipotential surfaces?

Similar Questions

Write the characteristics of equipotential surface.

What is an equipotential surface? Draw equipotential surfaces for:
$(1)$ $A$ single point charge
$(2)$ $A$ dipole (charges $+q$ and $-q$ at a small distance)
$(3)$ Two $+q$ charges at a small distance
$(4)$ $A$ uniform electric field.

Surfaces $A$ and $B$ are at the same potential $V'$. The work done in moving a charge $q$ from $A$ to $B$ is ........

Assertion $(A)$: In a region of constant potential,the electric field is zero and there can be no charge inside the region.
Reason $(R)$: According to Gauss's law,the charge inside the region should be zero if the electric field is zero.

The figure shows two equipotential lines in the $XY$ plane for an electric field. The scale is shown. The $X$-component $E_x$ and $Y$-component $E_y$ of the electric field in the space between the equipotential lines are respectively:

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