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  • (i) Use Gauss's law to find the electric field due to a uniformly charged infinite plane sheet. What is the direction of field for positive and negative charge densities? (ii) Find the ratio of the potential differences that must be applied

(i) Use Gauss's law to find the electric field due to a uniformly charged infinite plane sheet. What is the direction of field for positive and negative charge densities?
(ii) Find the ratio of the potential differences that must be applied across the parallel and series combination of two capacitors C1 and C2 with their capacitances in the ratio 1 : 2 so that the energy stored in the two cases becomes the same.

 

 

 

 
 
 
 
 

Answers (1)


Consider a large plain sheet of charge density \sigma and area A
Also, consider a cylindrical gaussian surface of crosssection s
The electric flux passes through two curved surfaces of the cylindrical surface by gauss law
flux

\phi = \int E\cdot dx= \frac{q}{\varepsilon _{0}}
    E\times 2S= \frac{\sigma S}{\varepsilon _{0}}
for positive \sigma is E is perpendicular outward the surface and for negative \sigma, E is inward perpendicular to the sheet
ii ) given

  \frac{1}{2}C_{s}V_{s}^2= \frac{1}{2}C_{p}V_{p}^{2}
           \frac{V_{s}}{V_{p}}= \sqrt{\frac{C_{p}}{C_{s}}}
                = \sqrt{\frac{C_{1}+C_{2}}{\frac{C_{1}C_{2}}{C_{1}+C_{2}}}}
              = \frac{C_{1}+C_{2}}{\sqrt{C_{1}C_{2}}}= \frac{3C_{1}}{\sqrt{2}C_{1}}
            =\frac{3}{\sqrt{2}}

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Safeer PP

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