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NCERT Class XII Chapter
Electric Charges and Fields
Questions With Solutions

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Question : 24 of 34
Marks: +1, -0
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 magnitudes 17.0 × 10−2210^{-22} C m−2m^{-2}. What is Electric field in
(a) the outer region of the first plate.
(b) the outer region of the second plate, and
(c) between the plates?
Solution:  
As both the plates have same surface charge density σ, so
EAE_A = EBE_B = σ2ε0\frac{\sigma}{2\varepsilon_0}
(a) In region-I, E1E_1 = EB−EAE_B - E_A = σ2ε0−σ2ε0\frac{\sigma}{2\varepsilon_0} - \frac{\sigma}{2\varepsilon_0} or E1E_1 = 0
(b) In region-III, EIIIE_{III} = EA−EBE_A - E_B = σ2ε0−σ2ε0\frac{\sigma}{2\varepsilon_0} - \frac{\sigma}{2\varepsilon_0} or EmE_m = 0
(c) In region-II, EIIE_{II} = EA+EBE_A + E_B = σ2ε0+σ2ε0\frac{\sigma}{2\varepsilon_0} + \frac{\sigma}{2\varepsilon_0} = σε0\frac{\sigma}{\varepsilon_0}
or EIIE_{II} = 17.0×10−228.85×10−12\frac{17.0 \times 10^{-22}}{8.85 \times 10^{-12}} = 1.92 × 10−1010^{-10} N C−1C^{-1}
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