Question

The variation of electric potential for an electric field is shown. Choose the option that represents the correct variation of electric field strength.

• A.
• B.
• C.
• D. None of the above

Answer 1

The correct option is B

As we know that relation between potential and electric field is given by

$E=-\frac{dV}{dr}$

So the regions where $dV=0$ or $V$ is constant, gives $E=0$

Apply above concept on different parts of the graph. So,

for region $\text{AB},$

$dV=V_B-V_A=20-10=10\text{V}$ and

$dr=r_B-r_A=0-(-2)=2\text{m}$

$\therefore E=-\frac{dV}{dr}=-\frac{10}{2}=-5\text{V/m}$

Similarly, for region $\text{BC}$ and $\text{EF},$

$\because dV=0$

$\therefore E=-\frac{dV}{dr}=0$

For region $\text{CD}$,

$dV=-10\text{V}$ and $dr=1\text{m}$

$\therefore E=-\frac{dV}{dr}=-\frac{-10}{1}=10\text{V/m}$

Similarly, for region $\text{DE}$

$E=-5\text{V/m}$

Only option (b) satisfy above calculated value.

So, option $\left(b\right)$ is correct.