Question

1. Two charged conducting spheres of radii R1

and R2

are at

same potential then the ratio of their charge densities is -

​

Answer 1

Answer:

hey mate....

refer to the attachment plz...

Answer 2

Solution:

Potential of a conducting sphere is given by:

$\boxed{V=\frac{KQ}{R}}$

∴ Potential due to first and second spheres are given by $\frac{KQ_1}{R_1}$ and $\frac{KQ_2}{R_2}$

Since they are at same potentials;

$\frac{KQ_1}{R_1}=\frac{KQ_2}{R_2}$

$\frac{Q_1}{R_1}=\frac{Q_2}{R_2}\\\\\boxed{\frac{Q_1}{Q_2}=\frac{R_1}{R_2}}----(1)$

Ratio of charge densities is given by :-

$=\frac{Q_1}{\frac{4}{3}\pi (R_1)^3} : \frac{Q_2}{\frac{4}{3}\pi (R_2)^3}$

$=\frac{Q_1}{ (R_1)^3} : \frac{Q_2}{ (R_2)^3}$

$=\boxed{\frac{Q_1}{ Q_2} . \frac{(R_2)^3}{ (R_1)^3}}----(2)$

From (1) and (2) ;

$\boxed{\boxed{Ratio=\frac{(R_2)^2}{ (R_1)^2}}}$

Hope this answer helped you :)