Question

An uncharged conducting large plate is placed as shown in the figure below. Now an electric field $E$ towards right is applied. Find the induced charge density on the right surface of the plate.

• A. $-{\epsilon }_{0}E$
• B. ${\epsilon }_{0}E$
• C. $-2{\epsilon }_{0}E$
• D. $2{\epsilon }_{0}E$

Answer 1

The correct option is B ${\epsilon }_{0}E$

When an uncharged conducting plate is kept in an external electric field, conductor gets polarised as shown in the figure.


Since, the net electric field is zero inside the conductor, we can say that electric field due to induced charges is equal to the applied electric field.

$i.eE=\frac{\sigma }{2{\epsilon }_0}+\frac{\sigma }{2{\epsilon }_0}=\frac{\sigma }{{\epsilon }_0}$

$\therefore$ Charge density on the right surface of the plate is $$\sigma ={\epsilon }_{0}E$$
Hence, option (b) is the correct answer.