SEM I 1516/BEE3113

UNIVERSITI MALAYSIA PAHANGFACULTY OF ELECTRICAL & ELECTRONICS ENGINEERING

BEE 3113 ELECTROMAGNETIC FIELDS THEORY

Assignment 1 – Electrostatic Fields (Group J,K) DUE DATE: 23/10/2015

1. Figure Q1 shows three charges exist in a free space. The first charge is a point charge at (0, 0, -2m). The second charge is an infinite line charge with

at x = -3m, y = 0m, and the third charge is an infinite sheet charge

with at y = -2m. Determine, at point P(1, 0, 1)(i) Electric field at point P due to the point charge, E1

(ii) Electric field at point P due to the line charge, E2(iii) Electric field at point P due to the surface charge, E3(iv) The total electric field at point P, ET

Figure Q1

2. Figure Q2 shows a point charge, Q = 2 µC at origin, surface charge at with the charge density given by and spherical volume charge in the

range of with the charge density .

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.(0, 0, -2)

x = -3, y = 0

y = -2

Q

y

x

z

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(i) Find D for , , and .(ii) Find where point P and Q are located at , .

Figure Q2

3. Electric flux density, C/m2 exists in the region of free space that includes a cylindrical volume enclosed by the region and height . Prove the divergence theorem by(i) Evaluating the volume integral side of the divergence theorem for the volume

defined above

(ii) Evaluating the surface integral of the corresponding closed surface.

4. Given the potential .

(i) Find the electric flux density D at .(ii) Calculate the work done in moving a 10µC charge from point A (5, 45°,90°)

to B (10, 90°, 45°)

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a

b

cz

y

xQ

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5. A point charges, Q located at the origin of the dielectric sphere shell as shown in Figure Q5. The dielectric constant of the shell is . Determine E, V, D and P for:

(i) r > ro

(ii) ri < r < ro

(iii) r < ri

Figure Q5

6. Figure Q6 shows a dielectric sphere shell surrounded by the conductor shell. Regions #1, #3 and #5 are a free space, region #4 is a dielectric with the relative permittivity of and region #2 is a conductor. Based on the assumption that there exists a point of Q in the spheres’ origin, obtain:

(i) D everywhere using Gauss law.(ii) E everywhere.

(iii) P everywhere.(iv) on the conductor surfaces.(v) on the dielectric surfaces.

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ri

ro

Q

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Figure Q6

7. Figure Q7 below shows a capacitor which is a sandwich three dielectric media.

For media 1, , media 2, and for media 3, . The thickness of

dielectric media 2 and 3 is given by d = 2 cm. The total plate area is A = 200 cm2.

The plate area for length is 100 cm2. By neglecting fringing.

(i) Calculating electric field intensity, E1, E2, and E3.

(ii) Calculate electric flux density, D1, D2, and D3.

(iii) Find the capacitance for plate area separated by media 1, C1.

(iv) Find the capacitance for plate area separated by media 2, and media 3, C2.

(v) Find the total capacitance.

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w

x

Q

r

y

z

#1

#2

#3

#4

#5

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Figure Q7

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Capacitor plate

d = 2 cm, E2, , D2

d = 2 cm, E3, , D3

E1,,

D1

E1,,

D1

10 V

Total length area = 200 cm2

Area = 100 cm2