Question

If the uniform surface charge density on the infinite plane sheet is $\sigma$, electric field near the surface will be

• A. $\frac{\sigma }{2{\epsilon }_0}$
• B. $\frac{3\sigma }{{\epsilon }_0}$
• C. $\frac{\sigma }{{\epsilon }_0}$
• D. $\frac{2\sigma }{{\epsilon }_0}$

Answer 1

Answer: (A)

Figure shows a portion of a flat thin sheet, infinite in size with constant surface charge density $\sigma$ (charge per unit area).
Let us draw a Gaussian surface (a cylinder) with one end on one side and other end on the other side and of cross-sectional area $S_0$. Field lines will be tangential to the curved surface, so flux passing through this surfaces is zero. At plane surface electric field has same magnitude and perpendicular to surface. Hence, using,
ES = $\frac{q_m}{{\epsilon }_0}$
$\therefore E(2S_0)=\frac{(\sigma )(S_0)}{{\epsilon }_0}$
$\therefore E\frac{(\sigma )(S_0)}{2{\epsilon }_0}$