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  • (a) Use Gauss’s theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density . (b) An in

(a) Use Gauss’s theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge
density \sigma.
(b) An infinitely large thin plane sheet has a uniform surface charge density +\sigma. Obtain the expression for the amount of work done in bringing a point charge q from infinity to a point, distant r, in front of the charged plane sheet.

 

 
 
 
 
 

Answers (1)

(a) Let the plane sheet be positivity charged

Let the gaussian surface be a cylinder of cross-sectional area A

\phi = E\times 2A

( the flux passes only through 2 circular cross-sections of the cylinder)

According to Gauss law

\phi =\frac{q}{\varepsilon _{o}}

E\times 2A=\frac{\sigma A}{\varepsilon _{0}}

E=\frac{\sigma }{2\varepsilon _{0}}

(b) The electric field E=\frac{\sigma }{2\varepsilon _{0}} is constant

  Work done w = fd

Displacement d = r

\therefore w=qEd=\frac{\sigma qd}{2\varepsilon_{0}}

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Safeer PP

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