$\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$
Faraday's Law of Induction Equation
Faraday's law of electromagnetic induction establishes the relationship between a changing magnetic field and the induced electric field (or electromotive force, EMF).
The mathematical representation of Faraday's law is:
$ \nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} $
This equation indicates that the curl of the electric field ($ \vec{E} $) is equal to the negative rate of change of the magnetic field ($ \vec{B} $) over time. This principle is fundamental to understanding electromagnetic induction.
Distinguishing Faraday's Law from Other Laws
The other equations presented represent different fundamental laws of electromagnetism:
- $ \nabla \bullet \vec B = 0 $: This is Gauss's law for magnetism, stating that magnetic monopoles do not exist.
- $ \nabla \bullet \vec D = \rho_v $: This is Gauss's law for electricity, relating the electric displacement field ($ \vec{D} $) to electric charge density ($ \rho_v $).
- $ \nabla \times \vec H = \sigma \vec{E} + \frac{\partial \vec{D}}{\partial t} $: This is the Ampere-Maxwell law, describing how electric currents and changing electric fields create magnetic fields.
Therefore, the equation $ \nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} $ specifically defines Faraday's law of electromagnetic induction.
Important Questions from Faraday's Law
In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell’s equations (in their standard form). Match the left-hand side with the corresponding right-hand side.
List I
List II
1.
∇. D
P
0
2.
∇ × E
Q
\(\rho_v\)
3.
∇. B
R
\( - \frac{{\partial B}}{{\partial t}}\)
4.
∇ × H
S
\(J+ \frac{{\partial D}}{{\partial t}}\)
“By the motion of the conductor or the coil in a magnetic field, i.e., the magnetic field is stationary and the moving conductors cut through it. The EMF generated in this way is normally called dynamically induced EMF.”
The given statement is specified by which of the following laws?
A flux of 0.25 mWb is produced by a coil of 1000 turns wound on a ring with a current of 2 A in it. Calculate the e.m.f induced in the coil when a current of 10 A is switched off, assuming the current will fall to zero in 1 millisecond.
Which of the following law states that “whenever the magnetic flux linked with a conductor or coil changes, an emf is induced in it?
All induction type transducers are based on
