The electric potential immediately outside a charged conducting sphere is 190 V,

Question

The electric potential immediately outside a charged conducting sphere is 190 V, and 10.0 cm farther from the center of the sphere the potential is 140 V.

(a) Determine the radius of the sphere.
cm

(b) Determine the charge on the sphere.
nC

The electric potential immediately outside another charged conducting sphere is 220 V, and 10.0 cm farther from the center the magnitude of the electric field is 360 V/m.

(c) Determine all possible values for the radius of the sphere. (Enter your answers from smallest to largest. If only one value exists, enter "NONE" in the second answer blank.)

(d) Determine the charge on the sphere for each value of r. (If only one value exists, enter "NONE" in the second answer blank.)

Explanation / Answer

a)
Vsphere = KQ/R

KQ/R = 190
KQ/R+0.1 = 140

=> 190R = 140(R+0.1)
=> R = 28 cm

b)
8.99*10^9*Q/0.2 = 190
=> Q = 4.23 nC

c)
|Esphere| = KQ/r^2

360 = KQ2/(r2+0.1)^2
220 = KQ2/r2

=> 360*(r2+0.1)^2 = 220r2
=> r2 = 0.385 m, 0.0259 m or 38.5 cm, 2.59 cm

d)
220*0.385 / 8.99*10^9 = Q2
=> Q2 = 9.42 nC
and
220*0.0259/8.99*10^9 = Q2
=> Q2 = 0.63 nC

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