Question

A uniform electric field having a magnitude E${}_0$ and direction along the positive x-axis exists. If the potential V is zero at x$=$ $0$, then its value at x $=$ $+x$ will be

• A. $V\left(x\right)=x^2{E}_0$
• B. $V\left(x\right)=-x^2{E}_0$
• C. $V\left(x\right)=-x{E}_0$
• D. $V\left(x\right)=x{E}_0$

Answer 1

The correct option is C $V\left(x\right)=-x{E}_0$

The uniform electric field is a constant field at every point.
now, $E=-\frac{dV}{dx}$

integrating, ${\int }_0^{V}dV=-E{\int }_0^{x_0}dx$
or $V=-E{x}_0$