Question

What does mean by energy stored in capacitor?
Prove that-
"The ratio of change in potentials of conductors after connecting two charged conductors is inversely proportional to their capacitances".
Draw a curve between electric field and distance for an uniformly for an uniformly charged non-conducting sphere.

Answer 1

Energy stored in a capacitor : A capacitor is a device to store energy. The process of charging up a capacitor involves the transferring of electric charges from its one plate to another.The work done in charging the capacitor is stored as its electrical potential energy. Consider two insulated conductor A and B of capacitance $C_1,C_2$ and carrying charges $Q_1$ and $Q_2$. Let $V_1$ and $V_2$ be their respective potentials.
$Q_1=C_1{V}_2$ and $Q_2=C_2{V}_2$
If connect with wire charge flow higher to lower potential
Total charge on system $Q_1+Q_2$
Total capacitance $C_1+C_2$
$V=\frac{Q}{C}=\frac{Q_1+Q_2}{C_1+C_2}=\frac{C_1{V}_1+C_2{V}_2}{C_1+C_2}$
$V\propto \frac{1}{C_1+C_2}$
Electric field distance curve by uniformly charged non- conducting sphere.
E outside $(r>r_0)$
$E=\frac{KQ}{r^2}$
$E$ inside $(r<r_0)$
$E=\frac{KQ.r}{r_0^3}$