Question

The electric field in a region of space is given by $\overrightarrow{E}=8x\hat{i}-4y\hat{j}-4z\hat{k}$. So, equation of lines of force in the plane, z = 0 is

• A. $2x-y=0$
• B. $xy=constant$
• C. $y^2+2x^2=constant$
• D. $\frac{x^2}{y}=constant$

Answer 1

The correct option is C $y^2+2x^2=constant$

Here, $E_x=8x,E_y=-4y,E_z=-4z$
For z = 0, $E_z=0$
$\frac{-dV}{dx}=8x,\frac{-dV}{dy}=-4y,\frac{dy}{dx}=-\frac{2x}{y}$
$\therefore \frac{y^2}{2}=\frac{-2x^2}{2}+constant$
$\Rightarrow y^2+2x^2=constant$