Engineering Electromagnetics (EE305)
Practice Set-I
August 25, 2020
Problem 1
Figure 1:
As shown in the Fig.1 a permanent magnet is present at the origin and their
are two current elements present at a certain distance from it such that magnetic
fields are parallel to the XZ and YZ plane. The current elements are aligned
in X and Y direction respectively with each having equal current I. Determine
which current element will rotate using common reasoning without using the
mathematical analysis or Faraday’s left and right hand rule.
Problem 2
As shown in the Fig.2 a permanent magnet is present at the origin and their
are two current carrying square loops present at a certain distance from it such
that magnetic fields are parallel to the XZ and YZ plane. The current loops are
aligned in YZ and XY plane respectively with each side having equal current I.
Determine which square loop will rotate using common reasoning without using
the mathematical analysis or Faraday’s left and right hand rule.
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Figure 2:
Figure 3:
Problem 3
Find the induced EMF in V-shaped loop making 60 degree angle with the x
axis as shown in Fig.3. Take B = 0.4az W/m2 and u = 2.8ax m/s and assume
that the sliding rode starts at the origin at t=0.
Figure 4:
Problem 4
A conducting bar is connected via flexible leads to a pair of rails in a magnetic
field B = 6 cos(10t)ax W b/m2 as shown in Fig.4. If the z axis is the equilibrium
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position of the bar and its velocity is 2 cos(10t)ay m/s. Find the voltage induced.
Problem 5
let f (x, y) = x3 y 3 .
(a) Find ∇f (x, y)
(b) Find derivative of f (x, y) in the direction of (1,2) at the point (3,2).
Problem 6
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Let f (x, y, z) = xyex +z −5 . Calculate the gradient of f (x, y, z) at point (1,3,-2)
and the directional derivative of f (x, y, z) at point (1,3,-2) in the direction of
vector v = (3,-1,4).
Problem 7
Why is the gradient considered the direction of the steepest ascent and what is
the condition of maximum directional derivative.
Problem 8
Concentric spherical shells of radii 2m, 4m and 8m carry uniform surface charge
densities of 20nc/m2 , −4nC/m2 and ρs nC/m2 respectively. The value of ρs (nC/m2 )
required to ensure that the Electric field flux is zero at 10 meter distance from
the center of the spherical shells.
Problem 9
You are an astronomical physicist residing currently in International Space Station (ISS). You along with your team have visualized giant magnetic field (Hfield) generated from earth whose equation has been determined by computational software as H = yz(x2 + y 2 ) x̂ + λy 2 xz ŷ + 4y 2 ẑ. where, x̂, ŷ and ẑ
are unit vectors along x, y and z axis. You are supposed to find the constant
λ which the computational software failed to find out using the concepts of
electromagnetic field theory.
Problem 10
For the fields given in Fig.5 determine the field equations assuming that the
proportionality is linear in nature and later intuitively guess whether the field
consists of divergence or curl or both. Later find mathematically using the
equations determined by you
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Figure 5:
Problem 11
Given three vectors A, B and C as follows
A = aˆx + 2aˆy − 3aˆz
B = −4aˆx + aˆz
C = 5aˆx − 2aˆz
find
(a) aA (b) |A − B| (c) A · B (d) θAB
(e) the component of A in the direction of C (f) A × C
(g) A · (B × C) and (A × B) · C
(h)A × (B × C) and (A × B) × C
Problem 12
Find the divergence of the following radial vector fields:
(a) f1 (R) = aR Rn
(b) f2 (R) = aR Rk2
Problem 13
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A vector field D = aR cosR3(φ) exists in the region between two spherical shells
defined
H by R = 1Hand R = 2. Evaluate
(a) D · ds (b) ∇ · D dv
Problem 14
Two electric charges q and −2q are placed at (0, 0) and (6, 0) on the XY plane
respectively. Find the equation of the zero potential curve in the XY plane.
Problem 15
Given the Electric field E = aφ sin φ2 . Find the magnetic field B in phasor form
using the relation ∇ × E = − ∂B
∂t .
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Figure 6:
Problem 15
For the assumed F(t) at R = 0 in Fig. 6. Sketch
(a)F(t-R/u) versus t
(b)F(t-R/u) versus R for t>T
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