Electromagnetic Fields GE-3, Class of 2022, ECEg-3053, Faculty of Comp & Elec…

Electromagnetic Fields

GE-3, Class of 2022, ECEg-3053, Faculty of Comp & Elec Eng’g, AMiT, AMU

Assignment 1

Due date: May 1, 2022

Direction

? Please, form a Group with a member of maximum 4 minimum 4 students. (Class

representative may facilitate the process). The left out students can be added to some

group as extra member.

? This assignment contain different types of questions from the concepts we covered the

practice you gain will be very valuable for your exam comes ahead.

? Every member of the group should participate in the process of solving problems. (There

will be some mechanism to check concept grasp of each student).

? Try to solve the problems neatly and show the details in good work flow. Sketch figures

whenever necessary to visualize the problem.

? All groups must submit their own work. Copying others group work fully or partially

leads to complete cancellation of assessment.

1. Let ? be the angle between the vectors A and B. What can be said about u if

(i) |A +B| < |A - B|, (ii) |A + B| = |A - B|, (iii) |A + B|.> |A – B|?

2. In a certain frame of reference with x-, y-, and z-axes, imagine the first octant to be

a room with a door. Suppose that the height of the door is h and its width is ?. The

top-right corner P of the door when it is shut has the rectangular coordinates

(?, 0, h).Now if the door is turned by angle ?, so we can enter the room, what are the

coordinates of P? What is the length of its diagonal r = OP in terms of ? and z? Suppose

the vector OP makes an angle ? with z- axis; express ? and h in terms of r and ?.

3. Apply the divergence theorem to evaluate ? ??. d??

.

??

, where A = x

2ax + y

2ay + z

2az and

S is the surface of the solid bounded by the cylinder ? = 1 and planes z = 2 and z = 4.

4. A vector field is given by

M =

v??

2+??2+??

2

v??

2+??2

[(?? – ??)???? + (?? + ??)????]

2 | P a g e

Figure 1

Evaluate the following integrals:

a. ? ??. ????

.

??

, where L is the circular edge of the volume in the form of an ice cream

cone shown in Figure above.

b. ? (?? ?? ?? ). ????

.

??1

, where S1 is the top surface of the volume

c. ? (?? ?? ?? ). ????

.

??2

, where S2 is the slanting surface of the volume

d. ? ??. ????

.

??1

e. ? ??. ????

.

??2

f. ? ??. ????

.

??

g. How do your results in parts (a) to (f) compare?

5. Four point charges are at the corners of a square of side a as shown in Figure 2. (a)

Determine the magnitude and direction of the electric field at the location of charge

q. (b) What is the resultant force on q?

Figure 2

6. An infinitely long line charge having a uniform charge per unit length ? lies a

distance d from point O as shown in Figure 3. Determine the total electric flux

through the surface of a sphere of radius R centered at O resulting from this line

charge. Consider both cases, where R > d and R

3 | P a g e

Figure 3

7. A uniformly charged disk has radius a and surface charge density s. Find

a. The electric potential

b. Electric field intensity along the perpendicular central axis of the disk.

Figure 4

8. For a spherical charge distribution

???? = {

???? (??

??-??

??) ,

(??

.

?? , (?? > ??)

.

Find,

a. E and V for r > a

b. E and V for r

c. Total charge in sphare

d. Show that E is maximum at r=0.145a

9. Find the energy stored in the hemispherical region r E = 2r sin ? cos ? ar + r cos ? cos ? a? – r sin ? a? V/m

exists.

4 | P a g e

10. A conducting sphere of radius a is half-embedded in a liquid dielectric medium of

permittivity e1, as in Figure 5. The region above the liquid is a gas of permittivity e2.

If the total free charge on the sphere is Q, determine the electric field intensity

everywhere.

Figure 5

“Hard work betrays none!”

Good luck !!!

Attachments: Assignment-I.pdfApr 26 2022 08:44 AM

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