Question

Figure shows two equipotential lines in $XY$ plane for an electric field. The $X$-component of the electric filed, $E_x$ and $Y$-component, $E_y$ in the space between these equipotential lines are respectively

• A. $-200{\text{V m}}^{-1};-100{\text{V m}}^{-1}$
• B. $-100{\text{V m}}^{-1};200{\text{V m}}^{-1}$
• C. $200{\text{V m}}^{-1};100{\text{V m}}^{-1}$
• D. $100{\text{V m}}^{-1};200{\text{V m}}^{-1}$

Answer 1

The correct option is B $-100{\text{V m}}^{-1};200{\text{V m}}^{-1}$


The slope of equipotential surfaces is,

$\tan \theta =\frac{1}{2}$

$\therefore \sin \theta =\frac{1}{\sqrt{5}}$ and $\cos \theta =\frac{2}{\sqrt{5}}$

The direction of the electric field is shown in the above figure and its magnitude is given by,

$E=\frac{\Delta V}{\Delta d}=\frac{4-2}{0.02\sin \theta }$

$=\frac{2}{0.02\times \frac{1}{\sqrt{5}}}=100\sqrt{5}{\text{V m}}^{-1}$

Now,

$E_x=-E\sin \theta =-100\sqrt{5}\times \frac{1}{\sqrt{5}}=-100{\text{V m}}^{-1}$

$E_y=E\cos \theta =100\sqrt{5}\times \frac{2}{\sqrt{5}}=200{\text{V m}}^{-1}$