1. A point charge Q with a velocity u = azuo enters a region having a uniform magnetic field
B =ax Bx+ ayBy + azBz . What E field should exist in the region so that the charge
proceeds without a change of velocity?
2. If vector A = ax 2+ ay3+ az4 and B = az5, what is the result of B×A?
3. Convert the point A (3, 60o, 5) into Cartesian coordinates. In which coordinate system is
A given.
4. The radial component of the radiated power density of an antenna in Watts per meter
squared is given by
sin 𝜃
𝑊𝑟𝑎𝑑 = 𝑎𝑅 𝐴 2
𝑅
Where “𝐴” is the peak value of the power density, θ is the usual spherical coordinate, and
aR is the radial unit vector. Evaluate the total radiated power in Watts if it is given by the
total outward flux of the radiated power density (Wrad).
5. Given that the electric field intensity of an electromagnetic wave in a nonconducting
dielectric medium is:
E = (2𝑎𝑦 + 3𝑎𝑧 )E0+e −αx
+
Where, Eo is the peak value of the Electric field intensity and α is the attenuation
⃗ and state the direction in
constant, find the associated magnetic field intensity vector, 𝐻
which the wave moves.
6. Starting from the Faraday’s Law, derive the homogeneous wave equation for a nonconducting source-free simple medium and show that the speed of light in free space is
3*10^8 m/s.
7. Determine the electric field intensity at P (- 0.2. 0. - 2.3) due to a point charge of +5 (nC)
at Q (0.2, 0.l, - 2.5) in air. All dimensions are in meters.
8. The maximum electric field intensity that a dielectric material can withstand without
breakdown is the dielectric strength of the material. If the dielectric strength of air is 3
x 106 V/m, Determine the amount of charge needed to cause air in earth’s atmosphere to
breakdown and become charged. Take Radius of Earth = 6.37 × 103 Km.
9. Assume a free charge density of -0.3 (nC/mm3) in a vacuum tube. For a current density
of -az2.4 (A/mm2), find (a) the total current passing through a hemispherical cap
specified by R = 5 (mm). (b) the velocity of the free charges.
10. An infinitely long, straight, solid, nonmagnetic conductor with a circular cross section of
radius b carries a steady current I. Determine the magnetic flux density both inside and
outside the conductor.
11. Given two point charges: q1 = 10(μC) at (2,0, - 4) and q2 = -60(μC) at (0, -1, -2),
determine
a) the electric field intensity at q 1 due to q2, and
b) the magnitude of the force experienced by q. All dimensions are in meters.
12. Do magnetic fields exist? Yes, or No? Explain your answer
13.