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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 17.0 × 10^–22 C/m2 . What is E: between the plates?

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?

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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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