Question

A sphere with a charge q is fixed at the bottom left corner of the right triangle shown in the figure. Points P and R are at the location shown. A test charge is place at point P, and the charge-sphere system has potential energy U0. If the test charge is then moved to point R, what will the potential energy of the charge-sphere system be? ​

Answer 1

Answer:

the final potential energy of this system is 3U0/10

Explanation:

We are given

charge at left end  and another test charge at point p

Potential energy is given by  = $\frac{k*Q1*Q2 }{R}$

where k is electrostatics constant = $9 *10^9$

Q1 = first charge , Q2=  test charge

R= distance between charges

potential at point p

U0 = k*Q1*Q2 /3 ⇒ kq1q2 = 3U0 ..............1

now the test charge moves to point R

using Pytahgoreou theorem

R(distance) = $\sqrt{8^2 + 6^2}$ = 10

New Potential energy

U1 = kq1*q2 / 10

substituting  kq1q2 = 3U0 from 1

U1 = 3U0/10

So this is the final potential energy of this system.