Question

Two infinitely large sheets having charge densities ${\sigma }_1$ and ${\sigma }_2$ respectively $({\sigma }_1>{\sigma }_2)$ are placed near each other separated by distance $d$.A charge $q$ is placed in between two plates such that there is no effect on charge distribution on plates. Now this charge is moved at an angle of ${45}^o$ with the horizontal towards plate having charge density ${\sigma }_2$ by distance $a$ $(a<d)$. Find work done by electric field in the process.

Answer 1

b'To find the work done on the electric field we need to find out the electric field of the given sheets.

thus the formula for finding the electric field can be directly given as:

$E=\frac{{\sigma }_1-{\sigma }_2}{2{ϵ}_0}$

then applying the formula of the electric field in the formula of work we get:

$W=qE.d$

to find $d$ refer the figure,

$\therefore d=\frac{a}{\sqrt{2}}$

substituting the value of $d$ in the equation of work we get,

$W=q\times E\times \frac{a}{\sqrt{2}}$

then again substituting the value of $E$ we get,

$W=\frac{q({\sigma }_1-{\sigma }_2)a}{2\sqrt{2}}{ϵ}_0$

'