The electric potential immediately outside a charged conducting sphere is 240 V,

Question

The electric potential immediately outside a charged conducting sphere is 240 V, and 10.0 cm farther from the center of the sphere the sphere the potential is 140 V. Determine the radius of the sphere. ____ cm Determine the charge on the sphere. ____ nC The electric potential immediately outside another charged conducting sphere is 250 V, and 10.0 cm farther from the center the magnitude of the electric field is 440 V/m. Determine all possible values for the radius of the sphere. (Enter your answers from smallest to largest. If only one value exists, enter "NONE" n the second answer blank.) r_1 = ____ cm r_2 = _____ cm Determine the charge on the sphere for each value of r. (If only one value exists, enter NONE in the second answer blank.) q_1 = _____ nC q_2 = _____ nC

Explanation / Answer

V = ke*Q / r
V(er=R) = 240 = ke*Q/R

V(er=R+0.10) = 140 = ke*Q / (R+0.1)

a)
So,
240/140 = (R+0.1)/R
R = 0.140 m(answer)

b) Q = 240R / Ke

= (240*0.140) / (8.99*10^9)
= 3.73*10^-9 C(Answer)

c) V(r=R) = 250 = KeQ/R

E(r=R+0.1) = 440=KeQ/(R+0.1)^2

250/440 = (R+0.1)^2/R

R = 0.021 , 0.52 cm

d)
For R = 0.021,
Q = 250R/Ke = 250(0.021)/(8.99*10^9)
= 0.59 nC

For R = 0.52 ,
Q = 250R/Ke = 250(0.52)/(8.99*10^9)
= 14.4 nC

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