Questions from Electronics

Q: (a) Check Eq. 5.76 for the configuration

(a) Check Eq. 5.76 for the configuration in Ex. 5.9. (b) Check Eqs. 5.77 and 5.78 for the configuration in Ex. 5.11.

Q: Prove Eq. 5.78, using Eqs. 5.

Prove Eq. 5.78, using Eqs. 5.63, 5.76, and 5.77. [Suggestion: I’d set up Cartesian coordinates at the surface, with z perpendicular to the surface and x parallel to the current.]

Q: Show that the magnetic field of a dipole can be written in

Show that the magnetic field of a dipole can be written in coordinate- free form:

Q: A circular loop of wire, with radius R, lies in

A circular loop of wire, with radius R, lies in the xy plane (centered at the origin) and carries a current I running counterclockwise as viewed from the positive z axis. (a) What is its magnetic dipo...

Q: Find the exact magnetic field a distance z above the center of

Find the exact magnetic field a distance z above the center of a square loop of side w, carrying a current I . Verify that it reduces to the field of a dipole, with the appropriate dipole moment, when z...

Q: (a) A phonograph record of radius R, carrying a

(a) A phonograph record of radius R, carrying a uniform surface charge σ , is rotating at constant angular velocity ω. Find its magnetic dipole moment. (b) Find the magnetic dipole moment of the spinn...

Q: I worked out the multipole expansion for the vector potential of a

I worked out the multipole expansion for the vector potential of a line current because that’s the most common type, and in some respects the easiest to handle. For a volume current...

Q: Analyze the motion of a particle (charge q, mass m

Analyze the motion of a particle (charge q, mass m) in the magnetic field of a long straight wire carrying a steady current I . (a) Is its kinetic energy conserved? (b) Find the force on the particle,...

Q: Calculate the Laplacian of the following functions: (a)

Calculate the Laplacian of the following functions: (a) Ta = x 2 + 2xy + 3z + 4. (b) Tb = sin x sin y sin z. (c) Tc = e−5x sin 4y cos 3z. (d) v = x 2 xˆ + 3xz2 yˆ− 2xz zˆ.

Q: Suppose that the magnetic field in some region has the form

Suppose that the magnetic field in some region has the form B = kz xˆ (where k is a constant). Find the force on a square loop (side a), lying in the yz plane and centered at the origin, if it carries...