Question

Two spheres have their surface charge density in the ratio 2:3 and their radii 3:2 the ratio of charges in them is

Answer 1

Answer:

Two spheres have their surface charge density in the ratio $2:3$ and their radii $3:2$ then the ratio of charges in them is $Q_1:Q_2=3:2$

Explanation:

The surface charge density $\sigma$ is the amount of charge $Q$ per unit area $A$,

$\sigma =\frac{Q}{A}$

The area of  the sphere having a radius $r$ is $A=4\pi r^2$

From the question ratio of surface charge densities $\sigma _1:\sigma _2=2:3$

and the ratio of their radii $r_1:r_2=3:2$

Now, charge of the sphere is $Q=\sigma A$

The ratio of charges of the spheres is $Q_1:Q_2=\sigma _1A_1:\sigma _2A_2$

After substituting the values given in the question

$\begin{array}{l}\frac{Q_1}{Q_2}=\frac{2\times 4\pi \left(3^2\right)}{3\times 4\pi \left(2^2\right)}\\\end{array}$

       $=\frac{3}{2}$

The ratio of their charges is $Q_1:Q_2=3:2$