1. Let potential V = 10x2 in free space, Find
(1)electric field E;
(2) volume charge density ?v;
(3) energy density;
(4) total energy within 1
2. A line current I flows along y axis from A(0,-3,0) to B(0,4,0). I is 2 A. Find:
(1) magnetic flux density B from Biot-Savart's Law at point P(2,8,-7);
(2) magnetic vector potential A at this point.
3. Conducting plates at z=5m and z=15m are held at potentials -10V and 10V, respectively. If the region between the plates is a homogeneous dielectric with epsilon= 2 epsilon(0), solving the Laplace equation to find:
(1) the potential distribution V(z) between two plates;
(2)the capacitance per unit area between the plates.
4. The electric field of a uniform plane wave propagating in lossless isotropic medium is
E(x,t) = 60(pi)cos(3 10 t + 4x) ay V/m. The magnetic field at point (0,0,0) when t = 0 is 1A/m. The unit of t is second and the unit of x is meter. Find:
(1) the phase velocity vp;
(2) the wave impedance (namda) of the media;
(3) the relative dielectric constant ?r and relative permeability (mu)r;
(4) the time domain expression for magnetic field;
5. The plane y = 2x separates two isotropic uniform materials. For y < 2x (region 1), (epsilon)r1 = 3; and for y > 2x (region 2), (epsilon)r2 = 5.
Assume D1 = 2ax - 3ay + 5az nC/m2 in region 1;
(1) Find the angle D2 makes with D1;
(2) Find E2 in region 2;