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### Electromagnetic Theory QUESTION BANK 131302

Electromagnetic Theory
QUESTION BANK
131302
UNIT I
PART A
1. What are the sources of electro magnetic fields?
2. Transform a vector A=yax-xay+zaz into cylindrical coordinates.
3. How the unit vectors are defined in cylindrical co-ordinate systems?
4. What is the physical significance of the term “divergence of a vector field”?
5. Define scalar triple product and state its characteristics.AIMFORHIGH
6. Give the relation between Cartesian and cylindrical co-ordinate systems
7. Define curl.
8. What is unit vector? What is its function while representing a vector?
9. Which are the differential elements in Cartesian co-ordinate system?
10. What is the physical significance of divergence?
11. Define Surface Integral.
12. Sketch a differential volume element in cylindrical co-ordinates resulting from differential changes in three orthogonal co-ordinate directions.
13. What is volume charge density?
14. Define Line Integral.
15. Calculate the total charge enclosed by a circle of 2m sides, centred at the origin and with the edge s parallel to the axes when the electric flux density over the cube is D=10x3/3ax(C/m2)
16. State stoke’s theorem.
17. Give practical examples for diverging and curling fields.
18. State Divergence theorem and mention the significance of the theorem.
19. A vector field F = (1/ r) ar in spherical co-ordinates. Determine F in Cartesian form at a point x =1, y =1 and z = 1.
20. Given A= 10 ay + 3az and B = 5ax + 4ay , find the projection of A on B
21. Prove that curl gradΦ = 0.
22. Verify that the vectors A = 4ax – 2ay + 2az and B = -6ax + 3ay – 3az are parallel to each other.
23. What are different co-ordinate systems?
24. The temperature in an auditorium is given by T= x2 + y2 – z. A mosquito located at (1, 1, 2) desires to fly in such a direction that it will get warm as soon as possible. In what direction it must fly?

PART B
1. (i) Explain the electric field distribution inside and outside a conductor
(ii) Explain the principle of electrostatic shielding.
(iii) Draw the equipotent lines and E lines inside and around a metal sphere.
2. i) State and prove Divergence theorem.
ii) State and prove Stokes theorem.
3. Given A = ax + ay, B = ax + 2az and C = 2 ay + az . Find (A X B) X C and compare
it with A X (B X C). Using the above vectors, find A.B X C and compare it with
A X B.C.
4. Find the value of the constant a, b, c so that the vector E = (x + 2y + az) ax +
(bx – 3y –2) ay + (4x + cy + 2z) az is irrotational.
5. Using the Divergence theory, evaluate ∫∫ E.ds = 4xz ax – y2 ay + yz az over the cube bounded by x = 0; x = 1; y = 0; y = 1; z = 0; z = 1.
6. Explain the spherical co-ordinate system?
7. (i) Use the cylindrical coordinate system to find the area of the curved surface of a
right circular cylinder where r = 20 m, h = 5m and 30º 120 º.
(ii)State and explain Divergence theorem.
8. (i) Derive the stoke’s theorem and give any one application of the theorem in electromagnetic fields
(ii)Obtain the spherical coordinates of 10ax at the point P (x = -3, y = 2, z = 4).
9. Find the charge in the volume

If ρ = 10 x2 y z μC/m3.
10. (i) Determine the constant c such that the vector F = (x + ay)i + (y + bz)j +
(x + cz)k will be solenoidal.
(ii) Given in cylindrical co-ordinate. For the contour shown
in Fig.Q-32, verify Stoke’s theorm.

Fig.Q-32.
11. Verify Stoke’s theorem for a vector field F = ρ2cos2 Φaρ+zsinΦaz around the
path L defined by 0≤ ρ ≤ 3, 0≤ Φ ≤ 45o and z = 0.
12. i) What are the major sources of Electromagnetic fields (any five)?
ii) What are the positive and negativeeffcts of EM fields on living things?
iii) What are the E and H field limits for public exposure?
iv)Give any one example to reduce the effect of EM field.
13. Verify the divergence theorem for a vector field A = xy2 ax+y3 ay+y2z az and
the surface is a cuboid defined by 0
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