A thin, uniformly charged spherical shell has a potential of 627 V on its surfac

Question

A thin, uniformly charged spherical shell has a potential of 627 V on its surface. Outside the sphere, at a radial distance of 16.0 cm from this surface, the potential is 416 V. Calculate the radius of the sphere. Determine the total charge on the sphere. What is the electric potential inside the sphere at a radius of 2.0 cm? Calculate the magnitude of the electric field at the surface of the sphere. If an electron starts from rest at a distance of 16.0 cm from the surface of the sphere, calculate the electron's speed when it reaches the sphere's surface.

Explanation / Answer

(a)
Given,
k*q/0.16 = 416
q = (416*0.16)/(8.9*10^9)
q = 7.47 * 10^-9 C

Potential at the Surface of a shell is given by, V = k*q/R
627 = (8.9*10^9 * 7.47 * 10^-9)/R
R = 0.106 m
Radius of the sphere, R = 10.6 cm

(2)
As calculate above, Total Charge on the sphere, q = 7.47 * 10^-9 C
or q = 7.47 nC

(3)
Potential inside the Shell is Constant and is equal to the Value at the Surface.
So, V inside the Sphere, = 627 V

(4)
Magneti Field at the Surface of the Sphere,
E = k*q/r^2
E = (8.9*7.47)/(0.106)^2
E = 5917 N/C

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