Question

A non-conducting square sheet of side 10 m is charged with a uniform surface charge density,$\sigma =-60\frac{\mu C}{m^2}$ . Find the magnitude and orientation of electric field vector due to the sheet at a point which is d = 0.02 mm away from the midpoint of the sheet.

• A. $3.39\times {10}^6\frac{N}{C}$, away from the sheet
• B. $6.78\times {10}^6\frac{N}{C}$, towards the sheet
• C. $3.39\times {10}^6\frac{N}{C}$, towards the sheet
• D. $6.78\times {10}^6\frac{N}{C}$, away from the sheet

Answer 1

The correct option is C

$3.39\times {10}^6\frac{N}{C}$, towards the sheet

For the point 0.02 mm away, the sheet may be treated as an infinite large sheet.

Do you concur?

So, $|\overrightarrow{E}|=\frac{\sigma }{2_{\epsilon }0}=\frac{1}{2}\frac{60\times {10}^{-6}}{8.85\times {10}^{-12}}\frac{N}{c}$

$=3.39\times {10}^6\frac{N}{c}$ [approx]

Since the charge on the sheet is negative, field direction will be towards the sheet.