Two large parallel plane sheets have uniform charge densities +\sigma and -\sigma. Determine the electric field (i) between the sheets, and (ii) outside the sheets.

 

 

Answers (1)
S safeer

Let us consider the two parallel sheets A and B of charges +\sigma and -\sigma and the points P,Q,R.

Now, the electric field due to the plane sheet of charge is given as 

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

Where, \sigma is the surface charge density.

Such that,

E_{A}=+\frac{\sigma }{2\varepsilon _{o}} and E_{B}=-\frac{\sigma }{2\varepsilon _{o}}

then,

(i) The electric field between the sheets at point Q is ;

\vec{E}=\vec{E}_A-\vec{E}_B

       =\frac{\sigma }{2\varepsilon _{o}}- (-\frac{\sigma }{2\varepsilon _{o}})

       =\frac{2}{2}(\frac{\sigma }{\varepsilon _{o}})

\vec{E}=\frac{\sigma }{\varepsilon _{o}}

(ii) The electric field outside the sheets at point P or P

\vec{E}=\vec{E}A+\vec{E}B

\vec{E}=\frac{\sigma }{2\varepsilon _{o}}- \frac{\sigma }{2\varepsilon _{o}}

\vec{E}=0

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