Question

TWO SPHERICAL CONDUCTORS EACH OF CAPACITY C ARE CHARGED TO A POTENTIAL V AND -V. THESE ARE THEN CONNECTED BY MEANS OF A FINE WIRE . THE LOSS OF ENERGY IS -
1. ZERO
2. 1/2CV^2
3. CV^2
4. 2CV^2

Answer 1

Answer on Question#40101, Physics, Electrodynamics

TWO SPHERICAL CONDUCTORS EACH OF CAPACITY C ARE CHARGED TO A POTENTIAL V AND -V. THESE ARE THEN CONNECTED BY MEANS OF A FINE WIRE. THE LOSS OF ENERGY IS -

1. ZERO 2. 1/2CV^2 3. CV^2 4. 2CV^2

Solution

The energy stored in the spherical conductor with positive potential is, $E_{1} = \left(\frac{1}{2}\right) CV^{2}$.

The energy stored in the spherical conductor negative potential is, $E_{2} = \left(\frac{1}{2}\right) C(-V)^{2} = \left(\frac{1}{2}\right) CV^{2}$.

Total energy of the system before conductors are connected is $E = E_{1} + E_{2} = \left(\frac{1}{2}\right) CV^{2} + \left(\frac{1}{2}\right) CV^{2} = CV^{2}$.

When the spherical conductors are connected total charge on the two conductors is zero because the spheres had equal and opposite charges

$$Q_{1} = CV, Q_{2} = C(-V) = -CV, Q_{system} = Q_{1} + Q_{2} = CV + (-CV) = 0.$$

And the potential becomes zero.

Hence, all the energy is lost. That is, the energy lost is $E_{\mathrm{lost}} = CV^2$.

Answer: 3. $CV^2$.