Question

The variation of potential $V$ with distance $r$ from a fixed point is shown in the figure. The magnitude of electric field at $r=2\text{cm}$ is

• A. $100\text{V/cm}$
• B. $200\text{V/cm}$
• C. $100\text{V/m}$
• D. $200\text{V/m}$

Answer 1

The correct option is D $200\text{V/m}$

The relation between electric field $\left(E\right)$ and electric potential $\left(V\right)$ is given by
$E=-\frac{dV}{dr}$
Here we can say that,
Electric field = Slope of the given graph between $0$ to $2\text{cm}$

For $0$ to $2\text{cm}$
$dV=4\text{V}-0\text{V}=4\text{V}$
and
$dr=(2-0)\text{cm}=2\text{cm}$
$\Rightarrow dr=0.02\text{m}$
So,
$E=-\frac{4}{0.02}=-200\text{V/m}$
The magnitude of electric field is $200\text{V/m}$

Hence, option (a) is correct.