Question

The magnitude of electric field due to an infinite uniformly charged insulating sheet is 10 N/C at a point which is at a distance 3m away from it. The surface charge density of the sheet will be?

• A. $\sigma =5{\epsilon }_{0}C/m^2$
• B. $\sigma =20{\epsilon }_{0}C/m^2$
• C. $\sigma ={\epsilon }_{0}C/m^2$
• D. None of these

Answer 1

The correct option is B

$\sigma =20{\epsilon }_{0}C/m^2$

The electric field due to an infinite uniformly charged insulating sheet at any point in space around it is given by $E=\frac{\sigma }{2{\epsilon }_0}$, provided that the point is not lying on the sheet itself.

Here it is given that E = 10 C/N

$\Rightarrow 10=\frac{\sigma }{2{\epsilon }_0}\Rightarrow \sigma =20{\epsilon }_0$

Note: Practically infinite sheet is impossible to make, but a point very near to a finite sheet can be treated as if lying near an infinite sheet and same approach can be applied. You will deal with similar kind of things thoroughly in capacitors.