ELECTROMAGNETICS
Tutorial: 4
Time Varying Fields
1. State and explain the Maxwell’s equation in differential and integral form. Also define
the displacement current and depth of penetration.
2. Write down the Maxwells equation in point from for time varying fields. Also explain
the meaning of each equation.
3. List out the Maxwell equations phasor form for the time varying case in free space. A
conducting bar can slide freely over two conducting rails placed at x = 0 and x = 10cm.
calculate the induced voltage in the bar if the bar slides at a velocity V = 10 ay m/s and
B = 3az mWb/m .
4. State and derive the expression of motional emf (electromotive force). Consider two
%⃗ = 6𝑎⃗z mWb/m2.
parallel conductors placed at x = 0 and x = 5 cm in a magnetic field 𝐵
A high resistance voltmeter is connected at one end and a conducting bar is sliding at
%⃗ = 18 𝑎⃗y m/s. calculate the induced voltage and show the
other end with velocity 𝑉
polarity of induced voltage across the voltmeter.
5. Find the amplitude of the displacement current density in an air space within a large
power transformer where H = 106(377t + 1.2566 × 10-6z) a A/m.
6. How does ∇ x H = J conflict with continuity equation in time varying fields. How is this
conflict rectified in such fields?
7. Show that the ratio of the amplitudes of the conduction current density and the
displacement current density is /ϵ for the applied field E = Em cost. Assume μ = μ .
8. Let μ = 3 x 10-5 H/m, ϵ = 1.2 x 10-10 F/m and = 0 everywhere. If H = 2cos(10 - βx)
a A/m, use Maxwell’s equations to obtain the expressions for B, D, E, β.
9. Distinguish between conduction and displacement currents.
10. Find the displacement current density
a) Next to your radio in air, where the local FM provides a carrier having H = 0.2cos
[2.10 (3 10 t – x)] az A/m
b) inside a large oil-filled power capacitor where ϵ = 6 and E = 100sin[ 1.257 (3
×10 t –2.45 z)] ax KV/m
c) In a typical metallic conductor at 60 Hz, where = 5 107 mho/m, ϵ =ϵ0 and J =
105sin[117.1(3.22t – z)] ax A/m2.
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y
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10t
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BY ER. SHIV SHANKAR SAH
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