Questions from Electronics

Q: Calculate ∇×E directly from Eq. 2.8, by

Calculate ∇×E directly from Eq. 2.8, by the method of Sect. 2.2.2. Refer to Prob. 1.63 if you get stuck.

Q: Find the electric field (magnitude and direction) a distance z

Find the electric field (magnitude and direction) a distance z above the midpoint between equal and opposite charges (±q), a distance d apart (same as Example 2.1, except that the charge at x = +d/2 is...

Q: One of these is an impossible electrostatic field. Which one?

One of these is an impossible electrostatic field. Which one? (a) E = k[xy xˆ + 2yz yˆ + 3xz zˆ]; (b) E = k[y2 xˆ + (2xy + z2) yˆ + 2yz zˆ]. Here k is a constant with the appropriate units. For the pos...

Q: Find the potential inside and outside a uniformly charged solid sphere whose

Find the potential inside and outside a uniformly charged solid sphere whose radius is R and whose total charge is q. Use infinity as your reference point. Compute the gradient of V in each region, and...

Q: Find the potential a distance s from an infinitely long straight wire

Find the potential a distance s from an infinitely long straight wire that carries a uniform line charge λ. Compute the gradient of your potential, and check that it yields the correct field.

Q: (a) Prove that the two-dimensional rotation matrix (

(a) Prove that the two-dimensional rotation matrix (Eq. 1.29) preserves dot products. (That is, show that (b) What constraints must the elements (Rij ) of the three-dimensional rotation matrix (Eq. 1...

Q: For the charge configuration of Prob. 2.15, find

For the charge configuration of Prob. 2.15, find the potential at the center, using infinity as your reference point.

Q: For the configuration of Prob. 2.16, find the

For the configuration of Prob. 2.16, find the potential difference between a point on the axis and a point on the outer cylinder. Note that it is not necessary to commit yourself to a particular referen...

Q: Using Eqs. 2.27 and 2.30, find

Using Eqs. 2.27 and 2.30, find the potential at a distance z above the center of the charge distributions in Fig. 2.34. In each case, compute E=-∇V, and compare your a...

Q: A conical surface (an empty ice-cream cone) carries

A conical surface (an empty ice-cream cone) carries a uniform surface charge σ. The height of the cone is h, as is the radius of the top. Find the potential difference between points a (the vertex) an...