Question

Two spheres have equal charges.Calculate the ratio of surface density of charge if the ratio of the volume density of charge is 8:64​

Answer 1

surface charge density ratio = 1:4

Answer 2

Given that,

The ratio of volume density of charge is 8 : 64​.

To find,

The ratio of surface density of charge.

Solution,

The ratio of volume charge density of the first sphere to the second sphere is given by :

$\dfrac{(q/4/3\pi r_1^3)}{(q/4/3\pi r_2^3)}=\dfrac{8}{64}\\\\\dfrac{r_2}{r_1}=\dfrac{1}{2}\ ...........(1)$

$r_1=2r_2$

The surface charge density of sphere is given by :

$\sigma=\dfrac{q}{4\pi r^2}$

For sphere 1 and 2 we get :

$\dfrac{(q/4\pi r_1^2)}{(q/4\pi r_2^2)}=\dfrac{r_1}{r_2}=\dfrac{1}{4}$

So, the ratio of the surface charge density of two sphere is 1:4.

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Surface charge density

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