Suppose we had a point charge q = +2.5 nC at the center of a dielectric shell of

Question

Suppose we had a point charge q = +2.5 nC at the center of a dielectric shell of inner radius R1 = 10 cm and outer radius 20 cm, surrounded by a spherical conducting shell of inner radius R2 = 20 cm and an outer radius R3= 25 cm, which has a total net charge of zero. The dielectric is uncharged and is made of polystyrene, with a dielectric constant of ?e = 2.6.

Find the electric potential at the outer surface of the dielectric shell.

Find the electric potential at the inner surface of the dielectric shell. (Hint: use what we know about dielectrics to determine the total E field inside the dielectric shell.)

Explanation / Answer

Answered By Mohsen

Find the electric potential at the outer surface of the dielectric shell.

V = kq/R = 9e9*2.5e-9/0.25 = 90 Volts

Find the electric potential at the inner surface of the dielectric shell.

V_inside the dielectric: kq/r = (1/(2.6*4*3.1416*8.85e-12)*2.5e-9/r = 8.6459/r

V = 90 + 8.6459/r = 90 + 8.6459/(0.20 - 0.10) = 176 Volts

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