Page 1 of 1
Problem Set #2
ECE 394 Problem Set 02
SHOW YOUR COMPLETE SOLUTIONS.
1. Given point charges Q nC each located at points A(1,1,0), B(1,-1,0), C(-1,1,0) and D (-1,-1,0) find the
following:
a) D at the origin
b) The amount of flux ψ passing through the y = 0 plane.
2. A sphere with radius 4 m carries a total charge of 7μC on its surface (uniformly distributed). Find the
electric field external to the sphere by using Gauss's law.
3. Solve for the divergence of:
a) 𝐃 = 20x𝑦2(𝑧 + 1)ax
+20𝑥2𝑦(𝑧 + 1)ay
+10𝑥2𝑦2az
b) 𝐃 = 4𝜌𝑧sin𝛷aρ
+ 2𝜌𝑧cos𝛷a𝛷
+ 2𝜌2sin𝛷 az
4. Given the flux density in space, find the total charge in the volume enclosed by
𝑟 =4 m ; 𝜃 = 𝜋
4 ; D
=5
3𝑟ar
C/m2
a) Draw the surface.
b) Use the differential form of Gauss’s Law to obtain the total charge.
c) Use the integral form of Maxwell’s first equation to obtain the total charge.
5. Given the Electric Field
E
=(𝑥
2+ 2𝑦)ax
+ 2𝑥ay
V/m
Find the work done in moving a 3C charge from the origin to the point P(-2, 1, 3) via the following paths:
a) From (0, 0, 0) to (-2, 0, 0) to (-2, 0, 3) to (-2, 1, 3)
b) Directly from (0, 0, 0) to (-2, 1, 3)
6. A point charge of 16 nC is located at Q(2, 3, 5) in free space, and a uniform line charge of 5 nC/m is at {x
= 2, y = 4}. If the absolute potential at the origin is 100 V, find V at P(4, 1, 3).
7. Given the potential field in free space:
𝑉 = 2(𝑥 + 1)2(𝑦 + 2)2(𝑧 + 3)2 𝑉
At P(2, -1, 4), find:
a) V
b) E
and |E
|
c) D
and |D
|
d) 𝜌𝑣
e) a𝑁
8. Find V at P(2, 3, 4) for an electric dipole located at the origin in free space has a moment
p
= 3a𝑥
− 2a𝑦
+ a𝑧
nC m
9. Find the energy stored in free space for the region 2mm < r < 3mm, 0 < 𝜃 < 90°, 0 < 𝛷 < 90°, given
the potential field
𝑉 = 200
𝑟 𝑉
