Explanation Given: The charge density is σ ( ϕ ) = a sin 5 ϕ . The infinite radius is R . Calculation: The given diagram is shown in Figure 1 Figure 1 The expression for the potential at a distance S in the cylindrical coordinate is given by, V ( s , ϕ ) = a 0 + b 0 ln s + ∑ K = 1 α s K ( a K cos K ϕ + b K sin K ϕ ) + s − K ( c K cos K ϕ + d K sin K ϕ ) The expression for the potential inside the cylinder is given by, V ( s , ϕ ) = a 0 + ∑ K = 1 α s K ( a K cos K ϕ + b K sin K ϕ ) The expression for the potential outside the cylinder is given by, V ( s , ϕ ) = a ¯ 0 + ∑ K = 1 α s 1 K ( c K cos K ϕ + d K sin K ϕ ) The boundary condition equation for the charge density is given by, σ = − ε 0 ( ∂ V o u t ∂ s − ∂ V i n ∂ s ) s = R | ∂ V o u t ∂ s | s = R = − K R K + 1 ( c K cos K ϕ + d K sin K ϕ ) | ∂ V i n ∂ s | s = R = K R K − 1 ( a K cos K ϕ + b K sin K ϕ ) σ = ∑ K = 1 α ( − K R K + 1 ( c K cos K ϕ + d K sin K ϕ ) − K R K − 1 ( a K cos K ϕ + b K sin K ϕ ) ) The comparison of above charge density with the given charge density is given by, σ = 5 ε 0 [ 1 R 6 d 5 sin 5 ϕ + R 4 sin 5 ϕ ] − ε 0 ( ∂ V

4th Edition

ISBN: 9781108420419

Author: David J. Griffiths

Publisher: Cambridge University Press

See similar textbooks

Question

Chapter 3.3, Problem 3.26P

To determine

The potential inside and outside the cylinder.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.3, Problem 3.25P

Chapter 3.4, Problem 3.27P

Students have asked these similar questions

Find the potential inside and outside a uniformly charged solid spherewhose radius is R and whose total charge is q. Use infinity as your reference point.Compute the gradient of V in each region, and check that it yields the correct field.Sketch V (r).

Find the electric potential at a distance h from the center of the mantle of a cylinder of radius R, with a distribution of homogeneous charge σ. Discuss the cases when h < R and when h > R

Using the Dirac-delta function, find the potential and electric field at the point (0,0,Z) of a homogeneously charged disk of radius a with total charge Q.

Chapter 3 Solutions

Introduction to Electrodynamics

Ch. 3.1 - Find the average potential over a spherical...Ch. 3.1 - Prob. 3.2P Ch. 3.1 - Prob. 3.3P Ch. 3.1 - Prob. 3.4P Ch. 3.1 - Prob. 3.5P Ch. 3.1 - Prob. 3.6P Ch. 3.2 - Find the force on the charge +q in Fig. 3.14....Ch. 3.2 - (a) Using the law of cosines, show that Eq. 3.17...Ch. 3.2 - In Ex. 3.2 we assumed that the conducting sphere...Ch. 3.2 - A uniform line charge is placed on an infinite...

Knowledge Booster

The potential inside and outside the cylinder.

Solution Summary: The equation for the potential inside and outside the cylinder is given by, V(s,varphi )=amathrmsin5.

The potential inside and outside the cylinder.

Want to see the full answer?

Chapter 3 Solutions