TUTORIAL 4 (SOLUTION)

EEE 3133

ELECTROMAGNETIC FIELDS AND WAVES

DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING

1. Find |E| at (0,3,4) m in Cartesian coordinates due to a point charge Q = 0.5µC at the

origin.

Ans: 180 V/m

2. A uniform line charge, infinite in extend, with ρl = 20nC/m, lies along the z axis. Find E

at (6,8,3) m.

Ans: 36 aρρρρ V/m

3. Refer to Figure 1. Point charge Q1 = 300µC, located at (1,-1,-3) m, experiences a force

18 8 4 N

x y zF a a a= − + due to point charge Q2 at (3,-3,-2) m. Determine Q2.

Ans: -40µµµµC

4. Find the charge in the volume defined by 0 ≤ x ≤ 1 m, 0 ≤ y ≤ 1 m, and 0 ≤ z ≤ 1 m if

ρ = 30 x2y (µC/m

3). What change occurs for the limits -1 ≤ y ≤ 0 m?

Ans: Q = 5µµµµC, Q = -5µµµµC

5. (a) Three point charges, Q1 = 30nC, Q2 = 150nC, and Q3 = -70nC are enclosed by

surface S. What net flux crosses S?

Ans: ΨΨΨΨnet = 110nC

(b) A circular disk of radius 4m with a charge density ρs = 12 sin φ µC/m2 is enclosed by

surface S. What net flux crosses S?

Ans: ΨΨΨΨnet = 0µµµµC

(c) Determine the flux crossing a 1mm by 1mm area on the surface of a cylindrical shell

at ρ=10m, z=-2m, φ=53.2° if

Ans = dΨΨΨΨ = -4µµµµC

22 2(1 ) 4 (C/ )x y z

D xa y a za m= + − +

6. For a line charge ρl = (10-9/2) C/m on the z axis, find VAB where A is (2m, π/2, 0) and B

is (4m, π, 5m).

Ans: 6.24V

7. Find the potential at rA = 5m with respect to rB = 15m due to a point charge Q = 500pC at

the origin and zero reference at infinity.

Ans: 0.6 V

8. Point charges Q1 = 1nC, Q2 = -2nC, Q3 = 3nC, and Q4 = -4nC are positioned one at a

time and in that order at (0,0,0), (1,0,0), (0,0,-1), and (0,0,1) respectively. Calculate the

energy in the system after each charge is positioned.

Ans: 0, -18nJ, -29nJ, -68.7nJ

From Practice Exercise 4.14 (Textbook)