# Q 1.24(c): Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17\times 10^{-22}\frac{C}{m^{2}}$. What is E:(c) between the plates?

We know, electric field, E, due to an infinite plate (length>>thickness) having surface charge density $\sigma$  =    $\sigma/\epsilon_{0}$ .

(To note: It's independent of distance from the plate!)

Let A and B be the two plates such that:

$\sigma_{A}= 17\times10^{-22} Cm^{-2}$ = $\sigma$

$\sigma_{B}= -17\times10^{-22} Cm^{-2}$ = - $\sigma$

Therefore,

The electric field between the plates,  E =   $E_{A} + E_{B}$ =  $\sigma_{A}/2\epsilon_{0} + (-\sigma_{B}/2\epsilon_{0})$

$= \sigma/2\epsilon_{0} = 17\times10^{-22}/8.85\times10^{-12} = 1.92\times10^{-10 } NC^{-1}$

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