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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Maxwell's equation derived from Faraday’s law is
Div(H) = J
Div(D) = I
Curl(E) = −dB/dt
Curl(B) = −dH/dt
Curl(E) = −dB/dt
Faraday’s law of electromagnetic induction states that a time-varying magnetic field induces an electromotive force (EMF). In differential form, this is expressed as the curl of the electric field intensity being equal to the negative time rate of change of the magnetic flux density.
Faraday’s law of electromagnetic induction states that a time-varying magnetic field induces an electromotive force (EMF). In differential form, this is expressed as the curl of the electric field intensity being equal to the negative time rate of change of the magnetic flux density.
∇×E=−∂t∂B — The differential form of Faraday's Law.
∮CE⋅dl=−dtd∬SB⋅dS — The integral form of Faraday's Law.
The principle relies on the generation of an electric field by a time-varying magnetic flux. As ∂t∂B changes, it produces a non-conservative electric field in space that opposes the change, represented by the negative sign in the equation (consistent with Lenz's Law).
The negative sign is a mathematical manifestation of Lenz's Law.
It demonstrates that electric fields are not always conservative in the presence of time-varying magnetic fields.
The equation is valid for both static and time-varying conditions, though for static fields, the right side becomes zero.
Explains the principle of operation for electrical transformers.
Fundamental in the design of electric motors and generators.
Does not account for source charges (requires Gauss's Law).
Only describes the interaction between E and B fields, not motion-induced EMF without considering Lorentz force.
Induction motors and generators.
Wireless power transfer systems.
Induction heating and electromagnetic sensors.
In SI units, E is in V/m and B is in Tesla (Wb/m2).
Option A (∇⋅H=J) is incorrect; the actual Maxwell equation is ∇×H=J+∂t∂D.
Option B (∇⋅D=I) is dimensionally incorrect; the correct form is ∇⋅D=ρv.
C is correct — Maxwell’s third equation, derived from Faraday’s law, is ∇×E=−∂t∂B.
Always remember the negative sign in the Faraday's law equation; it is a favorite for competitive exams to test your knowledge of Lenz's law.