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(A) In a uniform electric field,the electric potential $V$ at a point $(x, y, z)$ is given by $V = -E \cdot r + C$,where $E$ is the electric field vec

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$2$

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(A) In a uniform electric field,the electric potential $V$ at a point $(x, y, z)$ is given by $V = -E \cdot r + C$,where $E$ is the electric field vector and $r$ is the position vector.For a uniform electric field directed along the $x$-axis,the potential depends only on the $x$-coordinate $(V = -Ex + C)$.Therefore,all points lying on a plane perpendicular to the electric field lines have the same electric potential.In the given figure,there are $4$ rows of $3$ points each,forming a grid of $12$ points.The shaded point is in the middle column.The points that have the same potential as the shaded point are those that lie on the same vertical line (perpendicular to the electric field lines).There are $3$ points in that vertical column,including the shaded point itself.Thus,there are $2$ other points that have the same electric potential as the shaded point.

There is a uniform electric field of intensity $E$ as shown in the figure. How many labelled points have the same electric potential as the fully shaded point?

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