A capacitor is formed from two concentric spherical conducting shells separated

Question

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 12.5 cm, and the outer sphere has radius 15.5 cm. A potential difference of 150 V is applied to the capacitor.

A) What is the energy density at r = 12.6 cm , just outside the inner sphere? (Answer should be in J/m3)

B) What is the energy density at r = 15.4 cm , just inside the outer sphere? (Answer should be in J/m3)

C) For a parallel-plate capacitor the energy density is uniform in the region between the plates, except near the edges of the plates. Is this also true for a spherical capacitor? (Yes or No)

Explanation / Answer

C = 4pi*eo/((1/R1) - (1/R2))

R1 = 12.5 cm , R2 =15.5 cm

C =(4*3.14*8.85*10^-12)/((1/0.125) - (1/0.155))

C = 7.2*10^-11 F

V = 150 V

A) r = 12.6 cm

Q = VC

E = Q/(4pi*r^2)

E = (150*7.2*10^-11)/(4*3.14*0.126*0.126)

E = 5.42*10^-8 N/C

electric energy density

u =(1/2)eoE^2

u = (0.5*8.85*10^-12*5.42*5.42*10^-16)

u = 1.3*10^-26 J/m^3

B) r =15.4 cm

E = Q/(4pi*r^2)

E = (150*7.2*10^-11)/(4*3.14*0.154*0.154)

E = 3.6*10^-8 N/C

u = (1/2)eoE^2

u = 0.5*8.85*10^-12*3.6*3.6*10^-16

u = 5.74*10^-27 J/m^3

(c) Yes

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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