The electric potential immediately outside a charged conducting sphere is 220 V,

Question

The electric potential immediately outside a charged conducting sphere is 220 V, and 10.0 cm farther from the center of the sphere the potential is 160 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 240 V, and 10.0 cm farther from the center the magnitude of the electric field is 450 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

V1 = kQ/R = 220 V

V2 = KQ/(R+10cm) = 160

V1/V2 = (R+10cm)/R = 220/160

160R + 1600 = 220R

R = 26.67 cm = 0.2667 m

part b )

V1 = kQ/R

Q = V1*R/k

Q = 6.5185 x 10^-9 C = 6.5185 nC

part c )

V = KQ/R = 240 V

E = KQ/(R+10cm)^2 = 450 V/m

V/E = (R+0.1m)^2 / R = 240/450

45*(R+0.1)^2 = 24R

45R^2 + 9R + 0.45 = 24R

45R^2 - 15R + 0.45 = 0

R = 0.033 m 0.3 m

r1 = 0.033 m

r2 = 0.3 m

part d )

if r1 = 0.033

q1 = V*r1/k

q1 = 8.8 x 10^-10 C = 0.88 nC

if r2 = 0.3 m

q2 = 8*10^-9 C = 8 nC

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.