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A sphere of radius R has a volume density of charge rho=kr, were r is the distance from the centre of the sphere and k is constant . The magnitude of the electric field which exists at the surface of the sphere is given by (epsilon_(0)= permittivity of free space) |
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Answer» `(4pikR^(4))/(3epsilon_(0))`  Volume of the shell , `dV=4pix^(2)dx` LET us draw a GAUSSIAN SURFACE od radius `r(rltR)`as shown in the figure above. Total charge enclosed by the Gaussian surface is `Q_("in")=int_(0)^(r)rhodV=int_(0)(r)kx4pix^(2)dx=4pikint_(0)^(r)x^(3)dx` `=4pik[(x^(4))/(4)]_(0)^(r)=pikr^(4)` According to Gaussa.s law `E4pir^(2)=(Q_("in"))/(epsilon_(0))orE4pir^(2)=(pikr^(4))/(epsilon_(0))` At the surface of the sphere , r=R `thereforeE=(kR^(2))/(4piepsilon_(0))` |
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