Department of Electrical and Electronics Engineering
National Institute of Technology, Surathkal, Karnataka
EE207 Electromagnetic Field Theory
Assignment- I (August 2026)
1) Given the vector field in ‘mixed’ coordinate variables as
2) Find the Laplacian of the scalar fields
a) 𝑈 = 𝑥 2 𝑦 + 𝑥𝑦𝑧 b) 𝑉 = 𝜌𝑧𝑠𝑖𝑛∅ + 𝑧 2 𝑐𝑜𝑠 2 ∅ + 𝜌2
c) 𝑓 = 𝑐𝑜𝑠𝜃𝑠𝑖𝑛∅𝑙𝑛𝑟 + 𝑟 2 ∅
3) A field is given as G = [25/ (x2 + y2)] (xax + yay). Find
(a) a unit vector in the direction of G at P (3, 4, −2)
(b) the angle between G and ax at P
4) The electric field at a point P, expressed in cylindrical coordinate system is
given by
Find the value of divergence of the field, if the location of the point P is given
by (1, 2, 3) in Cartesian coordinate system.
5) Express the uniform vector field F = 5ax in (a) cylindrical components; (b)
spherical components
6) Express the unit vector ax in spherical components at the point: (a) r = 2, θ =
1 rad, φ = 0.8 rad; (b) x = 3, y = 2, z = -1; (c) ρ = 2.5, φ = 0.7 rad, z = 1.5
7) The Plane x = 10 carries a current of 100 mA/m along az, while line x= 1,
y = -2 carries a filamentary current of 20ℿ mA along az. Determine H at (4, 3, 2)
8) An infinitely long conductor is bent into an L shape as shown in Fig. 1. If a
direct current of 5 A flows in the conductor, find the magnetic field
intensity at (a) (2, 2, 0), (b) (0, -2, 0), and (c) (0, 0, 2)
Fig. 1
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9) Find H in rectangular components at P(2, 3, 4) if there is a current filament
on the z axis carrying 8 mA in the az direction. (b) Repeat if the filament is
located at x = -1, y = 2. (c) Find H if both filaments are present.
10) A current sheet K = 8ax A/m flows in the region -2 < y < 2 in the plane z = 0.
Calculate H at P(0, 0, 3).
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