A charge of 11 nC is uniformly distributed around a thin pla

A charge of -11 nC is uniformly distributed around a thin plastic ring lying in a yz plane with the ring center at the origin. A -7.8 pC pointt charge is located on the x axis at x = 3.0 m. For a ring radius of 2.1 m, how mu Ch work must an external force do on the pointt charge to move it to the origin? Number Units the tolerance is +/-9percentagee

Solution

The electric potential at any point at a distance of x from the origin of the ring is,

       Vx = kq₀ / sqrt(x^2 + r^2).

The potential at the centre of the ring is,

       Vo = kq₀ / r

Potential at a distance of x1 is

       Vx1 = kq₀ / sqrt(x1^2 + r^2).

the potential difference between these points is,

     Vo - Vx1 = kq₀ [(1/r) - (1/sqrt(x1^2 + r^2))]

the work done is,

            W = q(Vo - Vx1)

                = q * kq₀ [(1/r) - (1/sqrt(x1^2 + r^2))]

                = (-7.8x10^-12)(9x10⁹)(-11x10^-12)[(1/2.1) - {1 / sqrt((2.1² + 3²))}]

                = 0.1568X10^-12 J

                = 0.1568 pJ