Questions from Electronics

Q: Find the average potential over a spherical surface of radius R due

Find the average potential over a spherical surface of radius R due to a point charge q located inside (same as above, in other words, only with z < R). (In this case, of course, Laplace’s equation do...

Q: A uniform line charge λ is placed on an infinite straight wire

A uniform line charge λ is placed on an infinite straight wire, a distance d above a grounded conducting plane. (Let’s say the wire runs parallel to the x -axis and directly above it, and the conductin...

Q: Two semi-infinite grounded conducting planes meet at right angles.

Two semi-infinite grounded conducting planes meet at right angles. In the region between them, there is a point charge q, situated as shown in Fig. 3.15. Set up the image conï¬...

Q: Two long, straight copper pipes, each of radius R,

Two long, straight copper pipes, each of radius R, are held a distance 2d apart. One is at potential V0, the other at V0 (Fig. 3.16). Find the potential everywhere. [Hint: Exploit the result of Prob....

Q: Let r be the separation vector from a fixed point (x

Let r be the separation vector from a fixed point (x r, yr, zr) to the point (x, y, z), and let r be its length. Show that (a) ∇(r2) = 2r. (b) ∇(1/r) = −rˆ/r2. (c) What is the general formula for ∇(rn...

Q: Find the potential in the infinite slot of Ex. 3.

Find the potential in the infinite slot of Ex. 3.3 if the boundary at x = 0 consists of two metal strips: one, from y = 0 to y = a/2, is held at a constant potential V0, and the other, from y = a/2 to...

Q: For the infinite slot (Ex. 3.3), determine

For the infinite slot (Ex. 3.3), determine the charge density σ(y) on the strip at x = 0, assuming it is a conductor at constant potential V0.

Q: A rectangular pipe, running parallel to the z-axis (

A rectangular pipe, running parallel to the z-axis (from −∞ to +∞), has three grounded metal sides, at y = 0, y = a, and x = 0. The fourth side, at x = b, is maintained at a specified potential V0(y)....

Q: A cubical box (sides of length a) consists of five

A cubical box (sides of length a) consists of five metal plates, which are welded together and grounded (Fig. 3.23). The top is made of a separate sheet of metal, insulated from the oth...

Q: Derive P3(x) from the Rodrigues formula, and check

Derive P3(x) from the Rodrigues formula, and check that P3(cos θ) satisfies the angular equation (3.60) for l=3. Check that P3 and P1 are orthogonal by explicit integration.