A thin, uniformly charged spherical shell has a potential of 702 V on its surfac

Question

A thin, uniformly charged spherical shell has a potential of 702 V on its surface. Outside the sphere, at a radial distance of 14.0 cm from this surface, the potential is 376 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 14.0 cm from the surface of the sphere, calculate the electron's speed when it reaches the sphere's surface.


I know this is alot, but I am sooooo lost and really confussed. Your help would be AMAZING and I would be incredibly grateful!! :)

Explanation / Answer

E = -?V/?r = -(376 - 702)/0.14 = 2328 N/C V1 = 702 = E r = = 2328 r, => r = V1/E = 702/2328 = 0.30 m V1 = kQ/r, => Q = rV1/k = 0.30*702/9x10^9 = 23.5x10^-9 C = 23.5 nC E = kQ/r² = 9x10^9(23.5x10^-9)/0.30² = 2350 N/C To find the velocity utilize the following well known kinematic eqn: v² = 2ar where. acceleration: a = F/m, and the electrostatic force: F = qE hence, v = 2(F/m)r = 2(qE/m)r v = v{2(qE/m)r} = v{[2(1.6x10^-19)*2350/(9.11x10^-31)]0.30… v = 15.7 *10^6 m/s

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