Q: A sphere of radius R carries a charge density ρ(r
A sphere of radius R carries a charge density Ï(r) kr (where k is a constant). Find the energy of the conï¬guration. Check your answer by calculating it in at least two diffe...
See AnswerQ: Find the electric field a distance z above the center of a
Find the electric ï¬eld a distance z above the center of a circular loop of radius r (Fig. 2.9) that carries a uniform line charge λ.
See AnswerQ: Find the gradients of the following functions: (a)
Find the gradients of the following functions: (a) f (x, y, z) = x 2 + y3 + z4. (b) f (x, y, z) = x 2 y3z4. (c) f (x, y, z) = ex sin(y) ln(z).
See AnswerQ: The electric potential of some configuration is given by the expression
The electric potential of some conï¬guration is given by the expression where A and λ are constants. Find the electric ï¬eld E(r), the charge density Ï&...
See AnswerQ: Find the potential on the rim of a uniformly charged disk (
Find the potential on the rim of a uniformly charged disk (radius R, charge density σ ). [Hint: First show that / for some dimensionless number k, which you can express as an integral. Then evaluate...
See AnswerQ: Two infinitely long wires running parallel to the x axis carry uniform
Two inï¬nitely long wires running parallel to the x axis carry uniform charge densities +λ and −λ (Fig. 2.54). (a) Find the potential at any...
See AnswerQ: In a vacuum diode, electrons are “boiled” off a
In a vacuum diode, electrons are “boiled†off a hot cathode, at potential zero, and accelerated across a gap to the anode, which is held at positive potential V0. T...
See AnswerQ: Imagine that new and extraordinarily precise measurements have revealed an error in
Imagine that new and extraordinarily precise measurements have revealed an error in Coulomb’s law. The actual force of interaction between two point charges is found to be where &Ici...
See AnswerQ: Suppose an electric field E(x, y, z)
Suppose an electric field E(x, y, z) has the form Ex = ax, Ey = 0, Ez = 0 where a is a constant. What is the charge density? How do you account for the fact that the field points in a particular directi...
See AnswerQ: All of electrostatics follows from the 1/r2 character of Coulomb’s
All of electrostatics follows from the 1/r2 character of Coulomb’s law, together with the principle of superposition. An analogous theory can therefore be constructed for Newton’s law of universal gra...
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