MCQ
Consider a uniform electric field in the $\hat{\text{Z}}$ direction. The potential is a constant:
- AIn all space.
- BFor any $x$ for a given $ z.$
- CFor any $y$ for a given $z.$
- ✓On the $x-y$ plane for a given $z.$
✓
Answer
Correct option: D.
On the $x-y$ plane for a given $z.$
We know, the electric field intensity E and electric potential V are
$\text{E}=-\frac{\text{dV}}{\text{dr}}$
Electric potential decreases inf the direction of electric field. The direction of electric field is always perpendicular to one equipotential surface maintained at high electrostatic potential to other equipotential surface maintained at low electrostatic potential.
The electric field in $z-$direction suggest that equipotential surfaces are in $x-y$ plane. Therefore the potential is a constant for any $x$ for a given $z$, for any $y$ for a given $z$ and on the $x-y$ plane for a given $z.$
$\text{E}=-\frac{\text{dV}}{\text{dr}}$
Electric potential decreases inf the direction of electric field. The direction of electric field is always perpendicular to one equipotential surface maintained at high electrostatic potential to other equipotential surface maintained at low electrostatic potential.
The electric field in $z-$direction suggest that equipotential surfaces are in $x-y$ plane. Therefore the potential is a constant for any $x$ for a given $z$, for any $y$ for a given $z$ and on the $x-y$ plane for a given $z.$
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