Question

two spheres of radii 5cm and 3cm are given charges on risk volume and 50 calling respectively and then connected by a wire calculate the loss of energy after connection​

Answer 1

Solution given:

Radius of small sphere[r]=5cm=0.05m

Radius of large sphere[R]=10cm=0.1m

capacitance of small sphere[c]=4πε0r

=
`4π*8.85×10^(-12)×0.05=5.56*10^(-12)F`

Charge for small sphere[Q1]=100C

Charge for small sphere[Q2]=50C

Potential difference [V1]=
`(charge)/(capacitance)=(100)/(5.56*10^(-12))=1.8×10^(13)`V

.

again

capacitance of small sphere[C]=4πε0R

=
`4π*8.85×10^(-12)×0.1=1.11*10^(-11)F`

Potential difference [V2]=
`(charge)/(capacitance)=(50)/(1.11*10^(-11))=4.5×10^(12)`V

Now

Loss of energy:

`(cC(V1-V2)^(2))/(2(c+C))`

=
`(5.56*10^(-12)*1.11*10^(-11)(1.8*10^(13)-4.5*10^(12))^(2))/(2(5.56*10^(-12)+1.11*10^(-11)))`

=25Joule