Two concentric spherical shells of radii R1 and R2, with R1<R2, are fixed with the following values of the electrostatic potential: φ(R1, θ) = φ1cosθ and φ(R2, θ) = φ2 where φ1 and φ2 are constants and θ is the usual polar spherical angle. Find the electrostatic potential for: a) r<R1, inside the inner shell b) r>R2, outside the outer shell c) R1<r<R2, between the two shells d) Find the surface charge density σ(θ) on each of the two shells.

Two concentric spherical shells of radii R1 and R2, with R1<R2, are fixed with the following values of the electrostatic potential: φ(R1, θ) = φ1cosθ and φ(R2, θ) = φ2 where φ1 and φ2 are constants and θ is the usual polar spherical angle. Find the electrostatic potential for: a) r<R1, inside the inner shell b) r>R2, outside the outer shell c) R1<r<R2, between the two shells d) Find the surface charge density σ(θ) on each of the two shells.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter8: Capacitance

Section: Chapter Questions

Problem 77CP: A spherical capacitor is formed from two concentric spherical conducting spheres separated by...

See similar textbooks

Similar questions

(a) What is the potential between two points situated 10 cm and 20 cm from a 3.0C point charge? (b) To what location should the point at 20 cm be moved to increase this potential difference by a factor of two?
At a certain distance from a charged particle, the magnitude of the electric field is 500 V/m and the electric potential is 3.00 kV. (a) What is the distance to the particle? (b) What is the magnitude of the charge?
From a distance of 10 cm, a proton is projected with a speed of v=4.0106 m/s directly at a large, positively charged plate whose charge density is =2.0105 C/m2. (See below.) (a) Does the proton reach the plate? (b) If not, how far from the plate does it turn around?
A spherical capacitor is formed from two concentric spherical conducting spheres separated by vacuum. Tire inner sphere has radius 12.5 cm and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor, (a) What is the capacitance of the capacitor? tb) What is the magnitude of the electrical field at r = 12.6 cm, just outside the inner sphere? (c) What is the magnitude of the electrical field at r = 14.7 cm, just inside the outer sphere? (d) For a parallel-plate capacitor the electrical field is uniform in the region between the plates, except near the edges of the plates. Is this also true for a spherical capacitor?
Two 5.00-nC charged particles are in a uniform electric field with a magnitude of 625 N/C. Each of the particles is moved from point A to point B along two different paths, labeled in Figure P26.65. a. Given the dimensions in the figure, what is the change in the electric potential experienced by the particle that is moved along path 1 (black)? b. What is the change in the electric potential experienced by the particle that is moved along path 2 (red)? c. Is there a path between the points A and B for which the change in the electric potential is different from your answers to parts (a) and (b)? Explain. FIGURE P26.65 Problems 65, 66, and 67.
The electrostatic potential due to a change distribution is given by V(r) = Aº edr where A and 2 are con- stants. The total charge enclosed within a sphere of radius 1/a, with its origin at r=0 is given by, 87 E,A (a) Απε,Α TE,A (b) (c) (d) 0 [JEST 2015] e e
Help tq
A dsik of radius R-1m and charge Q-1mC is homogeneously charged. Find the electric potential at the rim of the disk. 2R dr A)9.5kV B)4.5kV C)27kV D)9.0OMV E)11.5kV
The electrostatic potential o(r) of a distribution of point charges has the form ø(r) cr-³ at a distance r from the origin (0,0,0), wherer»a.Which of the following distributions can give rise to this potential ? (0,0,0) (0,0,0) (a) (b) [TIFR 2015] -9 b. a a (0,0,0) (0,0,0) (c) (d) -g b. b- a
A rod of length L = 0.15 m is placed along the x-axis with its center at the origin. The rod has a non-uniform linear charge density of 2 = kịx| C/m, where k = 2.05E-12 C/m? is a у-аxis constant factor. Yob Х-аxis dq Otheexper PA What is the value of the potential at the point (0, yob) in volts if yob= 3.1 m? Grade Summ V(0,yob) = Deductions Potential tan() 7 8 sin() cos() HOME Submissions Attempts rem (5% per atten detailed view cotan() asin() acotan() acos() E 4 atan() sinh() 2 3 cosh() tanh() cotanh() + END Degrees Radians VIBACKSPACE DEL CLEAR Feedback I give up! Submit Hint
Parl D Constants A cylindrical capacitor has an inner conductor of radius 2.8 mm and an outer conductor of radius 3.2 mm. The two conductors are separated by vacuum, and the entire capacitor is 2.5 m long. The potential of the inner conductor relative to that of the outer conductor is 320 mV. Find the charge (magnitude and sign) on the inner conductor. Express your answer with the appropriate units. μA ха Хь ماه a b X.10n ☑ Q1= 336 C Submit Previous Answers Request Answer × Incorrect; Try Again; 3 attempts remaining Check that you have converted between SI units of electric charge correctly. Part C The potential of the inner conductor relative to that of the outer conductor is 320 mV. Find the charge (magnitude and sign) on the outer conductor. Express your answer with the appropriate units. HA ? Q2 Value Units
In a certain region of space, the electrical potential is given by the relationV(x,y,z) = Axy – Bx2 + Cywhere A, B, and C are positive constants. Calculate the x, y, and z components of the electric field.