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  • (a) Use Gauss’s law to show that due to a uniformly charged spherical shell of radius , the electric field at any point situated outside the shell at a distance <img alt="r" sr

(a) Use Gauss’s law to show that due to a uniformly charged spherical shell of radius R, the electric field at any point situated outside the shell at a distance r from its centre is equal to the electric field at the same point, when the entire charge on the shell were concentrated at its centre. Also plot the graph showing the variation of electric field with r, for r\leq R and r\geq R.

(b) Two point charges of +1\; \mu C and +4\; \mu C are kept 30\; cm apart. How far from the +1\; \mu C charge on the line joining the two charges, will the net electric field be zero ?

 

 

 

 
 
 
 
 

Answers (1)

a)

Consider a point P outside the shell at a distance r. Consider a spherical Gaussian surface of radius r.

Then  by Gauss law :

Flux enclosed by the surface

\phi =\oint E.ds=\frac{q}{\varepsilon _{o}}

E\times 4\pi r^{2}=\frac{q}{\varepsilon _{o}}

E = \frac{q}{4\pi \varepsilon _{o}r^{2}}

 

b)

Let the electric field be zero at x cm from 1micro coulomb charge

At p the electric field due to 1 and 2 are in the opposite direction

\\E_1-E_2=0\\\frac{kq_1}{x^2}=\frac{kq_2}{(30-x)^2}\\\\\frac{k1\mu C}{x^2}=\frac{k4\mu C}{(30-x)^2}\\\\30-x=2x\\\\x=10cm

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Safeer PP

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