Q: You can use the superposition principle to combine solutions obtained by separation
You can use the superposition principle to combine solutions obtained by separation of variables. For example, in Prob. 3.16 you found the potential inside a cubical box, if five faces are grounded and...
See AnswerQ: A conducting sphere of radius a, at potential V0, is
A conducting sphere of radius a, at potential V0, is surrounded by a thin concentric spherical shell of radius b, over which someone has glued a surface charge σ(θ) = k cos &I...
See AnswerQ: A charge +Q is distributed uniformly along the z axis from
A charge +Q is distributed uniformly along the z axis from z = −a to z = +a. Show that the electric potential at a point r is given by for r > a.
See AnswerQ: A long cylindrical shell of radius R carries a uniform surface charge
A long cylindrical shell of radius R carries a uniform surface charge σ0 on the upper half and an opposite charge σ0 on the lower half (Fig. 3.40). Find the electric potential in...
See AnswerQ: A thin insulating rod, running from z=-a to z
A thin insulating rod, running from z=-a to z=+a, carries the indicated line charges. In each case, find the leading term in the multipole expansion of the potential: (a) λ k cos(π z/2a), (b) λ k sin...
See AnswerQ: Show that the average field inside a sphere of radius R,
Show that the average ï¬eld inside a sphere of radius R, due to all the charge within the sphere, is / where p is the total dipole moment. There are several ways to prove this delight...
See AnswerQ: (a) Using Eq. 3.103, calculate the
(a) Using Eq. 3.103, calculate the average electric ï¬eld of a dipole, over a spherical volume of radius R, centered at the origin. Do the angular integrals ï¬rst. [Note:...
See AnswerQ: In Ex. 3.9, we obtained the potential of
In Ex. 3.9, we obtained the potential of a spherical shell with surface charge σ(θ) k cos θ . In Prob. 3.30, you found that the field is pure dipole out- side; it’s uniform inside (Eq. 3.86). Show that...
See AnswerQ: In two dimensions, show that the divergence transforms as a scalar
In two dimensions, show that the divergence transforms as a scalar under rotations. [Hint: Use Eq. 1.29 to determine and the method of Prob. 1.14 to calculate the derivatives. Your aim is to show tha...
See AnswerQ: Prove that the field is uniquely determined when the charge density ρ
Prove that the field is uniquely determined when the charge density ρ is given and either V or the normal derivative ∂V /∂n is specified on each boundary surface. Do not assume the boundaries are conduc...
See Answer
