Questions from Electronics

Q: Charge density σ(φ) = a sin 5φ

Charge density σ(φ) = a sin 5φ (where a is a constant) is glued over the surface of an infinite cylinder of radius R (Fig. 3.25). Find the potential ins...

Q: A sphere of radius R, centered at the origin, carries

A sphere of radius R, centered at the origin, carries charge density where k is a constant, and r , θ are the usual spherical coordinates. Find the approximate potential for points on the...

Q: A circular ring in the xy plane (radius R, centered

A circular ring in the xy plane (radius R, centered at the origin) carries a uniform line charge λ. Find the first three terms (n =0, 1, 2) in the multipole expansion for V (r,θ).

Q: Four particles (one of charge q, one of charge 3q

Four particles (one of charge q, one of charge 3q, and two of charge -2q) are placed as shown in Fig. 3.31, each a distance  from the origin. Find a simple approximate formula for t...

Q: Find the general solution to Laplace’s equation in spherical coordinates, for

Find the general solution to Laplace’s equation in spherical coordinates, for the case where V depends only on r . Do the same for cylindrical coordinates, assuming V depends only on s.

Q: In Ex. 3.9, we derived the exact potential

In Ex. 3.9, we derived the exact potential for a spherical shell of radius R, which carries a surface charge σ = k cos θ. (a) Calculate the dipole moment of this charge distribution. (b) Find the appr...

Q: Calculate the divergence of the following vector functions: (a

Calculate the divergence of the following vector functions: (a) va = x 2 xˆ + 3xz2 yˆ − 2xz zˆ. (b) vb = xy xˆ + 2yz yˆ + 3zx zˆ. (c) vc = y2 xˆ + (2xy + z2) yˆ + 2yz zˆ.

Q: For the dipole in Ex. 3.10, expand 1

For the dipole in Ex. 3.10, expand 1/r± to order (d/r)3, and use this to determine the quadrupole and octopole terms in the potential.

Q: Two point charges, 3q and -q, are separated by

Two point charges, 3q and -q, are separated by a distance a. For each of the arrangements in Fig. 3.35, find (i) the monopole moment, (ii) the dipole moment, and (iii) the approximat...

Q: A “pure” dipole p is situated at the origin,

A “pure” dipole p is situated at the origin, pointing in the z direction. (a) What is the force on a point charge q at (a, 0, 0) (Cartesian coordinates)? (b) What is the force on q at (0, 0, a)? (c) H...