Two circular loops of radii `0.05` and `0.09 m`, respectively, are put such that their axes coincide and their centers are `0.12 m` apart. A charge of `10^-6 C` is spread uniformly on each loop. Find the potential difference between the centers of the loops (in kV).

Answer

71

Explanation

The potential at the center of a ring will be due to charge on both the ring and as every element of a ring is and as every element of a ring is at a constant distance from the center ,so
`V_(1)=(1)/(4piepsilon_(0))[(q_(1))/(R_(1))+(q_(2))/(sqrt(R_(2)^(2)+x^(2)))]`
`=9xx10^(9)[(10^(-4))/(5)+(10^(-4))/(sqrt(9^(2)+12^(2)))]`
` =9xx10^(5)[(1)/(5)+(1)/(15)]=2.40xx10^(5)V`
Similarly `V_(2)=(1)/(4piepsilon_(0))[(q_(2))/(R_(2))+(q)/(sqrt(R_(1)^(2)+x^(2)))]`
or `V_(2)=9xx10^(3)[(1)/(9)+(1)/(13)]=(198)/(117)xx10^(5)`
`V_(2)=1.69xx10^(5)V`
so `V_(1)-V_(2)=(2.40-1.69)xx10^(5)=71kV`