1bt why ∫E.DS=E*4ΠR2
an electic field converges at the origin whose magnitude is given by the expression E=100r
Nt/Coul,where r is dist.measured from origin.
a)total charge contained in any spherical vol. with its centre at origin is -ve
b)total charge contained at any spherical vol.,irrespective of the location of its centre ,is -ve
c)total charge contained in a spherical vol. of radius 3cm with its centre at origin has magnitude 3x10power(-13)C
ans a,b,c
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8 Answers
1well as it converges the charge contained in any spherical vol
has to be negative(otherwise it will diverge in case of +ve charge)
further for any spherical volume of radius r applying gauss law q/ε0=-E*4πr2 as E=100r
we get q as a function of r
it is always negative suggesting that we have -ve charge everywhere
well one thing i must add to make it complete
let the charge at a distance x be dq
then the field contributed by it at a distance r=
kdq/r2
=kλ4πx2/r2
apply newton leibnitz rule and then you will get lambda
62This is a application of gauss law...
try to think a bit..
It is not very easy ..
but dont think anythign other than guass law.
another hint
take q(r) function of charge density with radius (origin)
62Yes E is a function of R
but E is also given to be constant at a fixed R
so ∫E.DS= E∫dS = E.S
because the integral is over the whole surface..