Question

12) The amount of electrical energy stored in a system of two charged particles a distance dd apart is

UE(d)=kq1q2/d

where particle 1 has charge q1, particle 2 has charge q2, and Coulomb's constant has the value k=k= 8.99×10⁹ N m22/C22.

Suppose that you have two particles of charge q1=7q1=7 nC and q2=−7q2=−7 nC. Let's say that you hold the positively charged particle in a fixed position while you steadily move the negatively charged particle farther and farther away at a constant speed of 3 m/s. The distance between the particles therefore changes according to the usual distance formula

d(t)=di+vt,

where v is the given speed and di=3 mm is their initial separation distance.

How much power do you deliver to the system at the time t=1s as you steadily separate the particles?

Answer 1

Initially the two charged particle was separated by 3 mm or 3 x 10^-3 m.

So, the initial energy of the two particle system was

                                        

After 1 second, the particle will travel 3 m.So, the new separation between the particles is

                                       

So, the change in energy = U_f -U_i = 146.7 x 10^-6 J

Since, the workdone= change in energy = 146.7 x 10^-6 J

So, the power delivered to the system in 1 second is

                                       

For any doubt please comment.