Dynamically induced EMF: When the conductor is rotating and the field is stationary, then the emf induced in the conductor is called dynamically induced EMF.
Ex: DC Generator, AC generator
Static induced EMF: When the conductor is in stationary and the field is changing (varying) then then the emf induced in the conductor is called static induced EMF.
Ex: TransformerDynamically induced EMF: When the conductor is rotating and the field is stationary, then the emf induced in the conductor is called dynamically induced EMF.
Ex: DC Generator, AC generator
Static induced EMF: When the conductor is stationary and the field is changing (varying) then the emf induced in the conductor is called static induced EMF.
Ex: TransformerWhich of the following law states that “whenever the magnetic flux linked with a conductor or coil changes, an emf is induced in it?
Faraday's laws: Faraday performed many experiments and gave some laws about electromagnetism.
Faraday's First Law:
Whenever a conductor is placed in a varying magnetic field an EMF gets induced across the conductor (called induced emf), and if the conductor is a closed circuit then induced current flows through it.
A magnetic field can be varied by various methods:
Faraday's second law of electromagnetic induction states that the magnitude of induced emf is equal to the rate of change of flux linkages with the coil.
According to Faraday's law of electromagnetic induction, the rate of change of flux linkages is equal to the induced emf:
\({\rm{E\;}} = {\rm{\;N\;}}\left( {\frac{{{\rm{d\Phi }}}}{{{\rm{dt}}}}} \right){\rm{Volts}}\)
Faraday's first law of electromagnetic induction:
It states that whenever a conductor is placed in a varying magnetic field, emf is induced which is called induced emf. If the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current.
Faraday's second law of electromagnetic induction:
It states that the magnitude of the voltage induced in the coil is equal to the rate of change of flux that linkages with the coil. The flux linkage of the coil is the product of number of turns in the coil and flux associated with the coil.
\(v=-N\frac{d\text{ }\!\!\Phi\!\!\text{ }}{dt}\)
Where N = number of turns, dΦ = change in magnetic flux and v = induced voltage.
The negative sign says that it opposes the change in magnetic flux which is explained by Lenz law.
Faraday’s Law states that a change in magnetic flux induces an emf in a coil.
Also, Lenz’s Law states that this induced emf produces a flux which opposes the flux that generates this emf, i.e.
\(emf=-\frac{d\phi }{dt}\) ---(1)
EMF is also defined as:
\(emf = \mathop \oint \nolimits_c \overset{\rightharpoonup}{E} .~\overset{\rightharpoonup}{{dl}}\)
Also, \(\phi ~\left( {Net~Flux} \right) = \mathop \smallint \nolimits_s \overset{\rightharpoonup}{B} .d\overset{\rightharpoonup}{s} \)
Putting the above in Equation (1), we get:
\(\mathop \oint \nolimits_c \overset{\rightharpoonup}{E} .d\overset{\rightharpoonup}{l} = - \frac{{\partial \phi }}{{\partial t}} = - \frac{\partial }{{dt}}\mathop \smallint \nolimits_s \overset{\rightharpoonup}{B} .d\overset{\rightharpoonup}{s}\)
\( \mathop{\int }_{S}\left( \nabla \times \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {E} \right).d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {s}=-\int \frac{\partial B}{\partial t}.d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {s}\)
\(\nabla \times \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {E}=-\frac{\partial B}{\partial t}\)
“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?
Concept of Dynamically or Motional Induced EMF by Faraday’s Second Law:
Consider a conductor of length 'l' is placed in magnetic field 'B' is move with velocity 'v' in such a way that all three are perpendicular to each other as shown,
Due to Faraday's 2^{nd} law, an EMF or current will be induced, and induced current will be opposite to cause due to Lenz's Law.
Now current or EMF induced will cause a force which is known as Magnetic force (Fm) is given by,
Fm = evB
Here the only e means the charge on an electron.
Since, the current is induced and hence electron (charge) also flow which further causes Force due to electric field and it is given by,
Fe = qE
At equilibrium, the force due to Electric Field will be equal to force due to Magnetic Field,
∴ Fe = Fm
or, qE = evB
Here the only also e means the charge on an electron.
Since, charge (q) = charge on electron (e)
∴ eE = evB
E = vB
We know that,
E = e/l
Now e is EMF induced
or, e/l = vB
Hence, \(e=Blv\)
Inductive transducers:
These works on the principle of change in inductance due to the quantity that is to be measured. These are basically two types.
They are based on Faraday's law.
Example: LVDT (Linear Variable Differential Transformer)
It measures the displacement in terms of the voltage difference between its two secondary voltages.
Faraday's law
It describes that the current will be induced in a conductor which is exposed to a change in a magnetic field. The direction of the current is given by Lenz's law.
Induced emf is given by:
\(e = -N \frac{d\phi}{dt}\)
Important Points
Seebeck effect: It is a phenomenon where the temperature difference between the two dissimilar electrical conductors produces a voltage. When the heat is applied to one conductor then the heated electrons flow from that to the other conductor.
Peltier effect: It is the reverse phenomenon of the Seebeck effect. The electrical current flowing through the junction connecting two materials will emit or absorb the heat per unit time at the junction to balance the difference in the chemical potential difference.
Concept:
According to Faraday's law, the induced emf in a coil (having N turns) is the rate of change of magnetic flux linked with coil,
\({\rm{e}} = {\rm{-N}}\frac{{{\rm{d}}ϕ }}{{{\rm{dt}}}}\)
N = number of turns in the coil
ϕ = magnetic flux link with the coil
Calculation:
Given that ϕ = (t^{2} – 3t) m-wb and N = 200
Induced emf in coil
\({\rm{e}} = {\rm{-N}}\frac{{{\rm{d}}ϕ }}{{{\rm{dt}}}}\)
\({\rm{e}} = -200\frac{{\rm{d}}}{{{\rm{dt}}}}\left( {{{\rm{t}}^2} - 3{\rm{t}}} \right)×10^{-3}\)
e = -200 (2t - 3) × 10^{-3}
then the induced emf in the coil at t = 4
e = - 200 (2 × 4 - 3) × 10^{-3 }= - 1 V
Faraday's laws: Faraday performed many experiments and gives some law about electromagnetism.
Faraday's First Law: Whenever a conductor is placed in a varying magnetic field an EMF gets induced across the conductor (called as induced emf), and if the conductor is a closed circuit then induced current flows through it.
A magnetic field can be varied by various methods –
Faraday's second law of electromagnetic induction states that the magnitude of induced emf is equal to the rate of change of flux linkages with the coil.
Where
E = Induced emf
N = Number of turns
\(\left( {\frac{{{\rm{d\Phi }}}}{{{\rm{dt}}}}} \right)\) = Rate of change in flux
Flux linkage:
ψ = N × ϕ
\(E= N\left( {\frac{{{\rm{d\Phi }}}}{{{\rm{dt}}}}} \right){\rm{}}\)
\(E = \left( {\frac{{{\rm{d\Phi N }}}}{{{\rm{dt}}}}} \right){\rm{}}\)
\(E=\left( {\frac{{{\rm{d\psi }}}}{{{\rm{dt}}}}} \right){\rm{}}\)
Faraday’s law of electromagnetic induction, the rate of change of flux linkage is equal to induced emf.
Choose the expression for Faraday's second Law of Electromagnetic Induction.
Note: ϵ is the electromotive force, ϕ is the magnetic flux, N is the number of turns
Faraday’s first law:
Faraday's second law:
Faraday's second law of electromagnetic induction states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil.
The flux linkage of the coil is the product of the number of turns in the coil and flux associated with the coil.
\(E = - N\frac{{d\phi }}{{dt}}\)
Important Points
Method to change the magnetic field:
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 |
\( \frac{{ - dB}}{{dt}}\) |
4. |
∇ × H |
S |
\(J + \frac{{dD}}{{dt}}\) |
Various Maxwell laws are shown in the table
Differential form |
Integral form |
1. \(\nabla .\vec D = \rho_v\) |
\(\oint \vec D.\vec ds = \mathop \smallint \limits_v^{} \rho_vdV\) |
2. \(\nabla \times \vec E = \frac{{ - dB}}{{dt}}\) |
\(\mathop \oint \limits_L^{} \vec E.\overrightarrow {dl} = \frac{{ - \partial }}{{dt}}\;\mathop \smallint \limits_s^{} \vec B.\overrightarrow {ds}\) |
3. \(\nabla .\vec B = 0\) |
\(\oint \vec B.\overrightarrow {ds} = 0\) |
4. \(\nabla \times \vec H = J + \frac{{dD}}{{dt}}\) |
\(\oint \vec H.\overrightarrow {dl} = \mathop \smallint \limits_s^{} \left( {\vec J + \frac{{d\vec D}}{{dt}}} \right)ds\) |
The correct answer is Faraday's law of electromagnetic induction.
Additional Information
Right-hand thumb rule |
When electricity (conventional current) flows in a long straight wire it creates a circular or cylindrical magnetic field around the wire. According to the right-hand rule. If the fingers of the right hand are curled in the direction of the circular component of the current, the right thumb points to the north pole. |
Fleming’s left-hand rule |
Fleming's left-hand rule states that When a current-carrying conductor is placed in an external magnetic field, the conductor experiences a force perpendicular to both the field and to the direction of the current flow. It was invented by John Ambrose Fleming. |
Fleming's right-hand rule |
Fleming's right-hand rule shows the direction of induced current when a conductor attached to a circuit moves in a magnetic field. When a conductor such as a wire attached to a circuit moves through a magnetic field. |
Faraday’s law of electromagnetic induction:
According to Faraday’s law of electromagnetic induction, the electromotive force (E) induced in each turn of wire in any circuit containing loops (as a coil) is related to the rate of change of the magnetic flux (ϕ) through it with the change in the time.
\(E = - \frac{{dϕ }}{{dt}}\)
The negative sign indicates the direction of E and hence the direction of the current in a closed loop.
For N turns, the emf will be
\(E = - N\frac{{dϕ }}{{dt}}\)
Additional Information
Nortons theorem: A liner bilateral network can be replaced by a single current source (Isc) in parallel with an equivalent impedance Zeq.
When Isc is the short circuit current flows through the load terminals & Zeq is the equivalent impedance across the open terminals of load.
Thevenin theorem: A liner bilateral network can be replaced by a single voltage source (Vth) in series with an equivalent impedance Zeq.
Where Vth is an open circuit voltage across the load terminals and Zeq is the equivalent impedance across the open load terminals.
Thevenin theorem is preferred in a circuit involving voltage source and series connection whereas Norton’s theorem is preferred in the circuits involving current source and parallel connections.