Q: (a) Suppose the potential is a constant V0 over the
(a) Suppose the potential is a constant V0 over the surface of the sphere. Use the results of Ex. 3.6 and Ex. 3.7 to find the potential inside and outside the sphere. (Of course, you know the answers i...
See AnswerQ: The potential at the surface of a sphere (radius R)
The potential at the surface of a sphere (radius R) is given by V0 = k cos 3θ, where k is a constant. Find the potential inside and outside the sphere, as well as the surface charge density σ(θ) on th...
See AnswerQ: In one sentence, justify Earnshaw’s Theorem: A charged particle cannot
In one sentence, justify Earnshaw’s Theorem: A charged particle cannot be held in a stable equilibrium by electrostatic forces alone. As an example, consider the cubical arrangement...
See AnswerQ: Suppose the potential V0(θ) at the surface of a
Suppose the potential V0(θ) at the surface of a sphere is specified, and there is no charge inside or outside the sphere. Show that the charge density on the sphere is given by / where /
See AnswerQ: Find the potential outside a charged metal sphere (charge Q,
Find the potential outside a charged metal sphere (charge Q, radius R) placed in an otherwise uniform electric field E0. Explain clearly where you are setting the zero of potential.
See AnswerQ: Suppose that f is a function of two variables (y and
Suppose that f is a function of two variables (y and z) only. Show that the gradient / transforms as a vector under rotations, Eq. 1.29. and the analogous formula for /. We know that / And / &...
See AnswerQ: In Prob. 2.25, you found the potential on
In Prob. 2.25, you found the potential on the axis of a uniformly charged disk: / (a) Use this, together with the fact that Pl (1) 1, to evaluate the first three terms in the expansion (Eq. 3.72) for...
See AnswerQ: A spherical shell of radius R carries a uniform surface charge σ0
A spherical shell of radius R carries a uniform surface charge σ0 on the “northern” hemisphere and a uniform surface charge σ0 on the “southern” hemisphere. Find the potential inside and outside the s...
See AnswerQ: Solve Laplace’s equation by separation of variables in cylindrical coordinates, assuming
Solve Laplace’s equation by separation of variables in cylindrical coordinates, assuming there is no dependence on z (cylindrical symmetry). [Make sure you find all solutions to the radial equation; in...
See AnswerQ: Find the potential outside an infinitely long metal pipe, of radius
Find the potential outside an infinitely long metal pipe, of radius R, placed at right angles to an otherwise uniform electric field E0. Find the surface charge induced on the pipe. [Use your result fro...
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