How much charge is on the surface of an isolated spherical conductor that has a

Question

How much charge is on the surface of an isolated spherical conductor that has a 9.0 cm radius and is charged to 2.30 kV? What is the electrostatic potential energy of this conductor? (Assume the potential is zero far from the sphere.) If a conducting sphere is to be charged to a potential of 8000 V, what is the smallest possible radius of the sphere such that the electric field will not exceed the dielectric strength of air? A spherical conductor of radius R_1 is charged to 29 kV. When it is connected by a long, very thin conducting wire to a second conducting sphere far away, its potential drops to 15 kV. What is the radius of the second sphere as a multiple of R_1?

Explanation / Answer

2a.

V = kQ/R

Q = VR/K

Q = 2300*0.09/(9*10^-9) = 23*10^-9 C

Q = 23 nC

1b. U = 0.5*QV

U = 0.5*23*2300*10^-9 = 2.645*10^-5 J

U = 26.45 uJ

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