Question

• Write an expression to find electric flux passing through small element ds
• Which law helps to find total flux passing through a closed surface? State the law.
• Using this law, derive an expression for electric field due to thin uniformly charged shell.
• How can we protect delicate instruments from external electric field?

Answer 1

1. \(d\phi=\overrightarrow E.d \overrightarrow s\)

2. Gauss’s law:

Guass’s law states that total flux over a closed surface is 1/s₀ times net charge enclosed by the surface.

3. Field due to A uniformly charged infinite plane sheet:

Consider an infinite thin plane sheet of change of density σ. 

To find electric field at a point P (at a distance ‘r’ from sheet), imagine a Gaussian surface in the form of cylinder having area of cross section ‘ds’. 

According to Gauss’s law we can write,

\(\int\overrightarrow E.d\overrightarrow s=\frac{1}{\varepsilon_0}q\)

\(E\int ds=\frac{\sigma ds}{\varepsilon_0}\)(Since q = σds)

But electric field passes only through end surfaces ,so we get ∫ds = 2ds

i.e. E2ds = \(\frac{\sigma ds}{\varepsilon_0}\)

\(E = \frac{\sigma ds}{2ds\varepsilon_0}\), \(E = \frac{\sigma }{2\varepsilon_0}\)

E is directed away from the charged sheet, if σ is positive and directed towards the sheet if σ is negative.