Faraday's Law MCQ Quiz - Objective Question with Answer for Faraday's Law - Download Free PDF
Last updated on Jun 19, 2025
Latest Faraday's Law MCQ Objective Questions
Faraday's Law Question 1:
In which situation will an EMF be induced in a conductor, according to Faraday's Laws?
Answer (Detailed Solution Below)
Faraday's Law Question 1 Detailed Solution
Faraday's Laws of Electromagnetic Induction
Definition: Faraday's Laws of Electromagnetic Induction describe how an electromotive force (EMF) is induced in a conductor when the magnetic flux linked with it changes. This principle is fundamental to the operation of many electrical devices, including electric generators, transformers, and induction motors.
Working Principle: According to Faraday's first law, an EMF is induced in a conductor when there is a change in the magnetic flux linked with it. Faraday's second law quantifies this phenomenon, stating that the magnitude of the induced EMF is proportional to the rate of change of magnetic flux through the conductor.
Mathematical Representation:
The induced EMF (ε) can be expressed as:
ε = -dΦ/dt
Where:
- ε: Induced EMF (volts)
- Φ: Magnetic flux (Weber)
- t: Time (seconds)
The negative sign in the equation represents Lenz's Law, which states that the induced EMF always opposes the change in magnetic flux that causes it.
Correct Option Analysis:
The correct option is:
Option 4: When there is relative motion between a conductor and a magnetic field.
When a conductor moves relative to a magnetic field, or when the magnetic field changes around a stationary conductor, the magnetic flux linked with the conductor changes. According to Faraday's Laws, this change in magnetic flux induces an EMF in the conductor. This is the fundamental principle behind the operation of electric generators, where the relative motion between a coil of wire (conductor) and a magnetic field generates electricity.
Example:
Consider a simple setup where a conductor is moved through a magnetic field:
- When the conductor moves through the magnetic field, the magnetic flux linking the conductor changes.
- This changing flux induces an EMF in the conductor, which can drive a current if the circuit is closed.
This principle is utilized in generators, where mechanical energy is converted into electrical energy by rotating a coil within a magnetic field, causing a relative motion and inducing an EMF.
Important Information:
To further understand the analysis, let’s evaluate the other options:
Option 1: When the temperature of the conductor increases.
An increase in temperature of a conductor does not induce an EMF. While temperature changes can affect the resistance of a conductor, they do not directly cause a change in magnetic flux, which is a prerequisite for the induction of EMF according to Faraday's Laws. Thus, this option is incorrect.
Option 2: When the conductor is stationary in a magnetic field.
If a conductor is stationary in a constant magnetic field, the magnetic flux linked with the conductor remains unchanged. As there is no change in magnetic flux, no EMF is induced. This principle highlights the necessity of relative motion or a changing magnetic field for the induction of EMF. Therefore, this option is also incorrect.
Option 3: When the magnetic field is constant.
A constant magnetic field does not induce an EMF in a stationary conductor. According to Faraday's Laws, an EMF is induced only when there is a change in magnetic flux. A constant magnetic field does not produce any such change, and hence, no EMF is induced. This makes this option incorrect as well.
Conclusion:
The induction of EMF in a conductor, as described by Faraday's Laws, requires a change in magnetic flux. This change can occur due to relative motion between the conductor and the magnetic field or due to a time-varying magnetic field. The correct option, therefore, is Option 4: "When there is relative motion between a conductor and a magnetic field." This principle is fundamental to the operation of many electrical machines and devices, making it a cornerstone of electromagnetic theory and practical applications in electrical engineering.
Faraday's Law Question 2:
In a series magnetic circuit, ___________ flux φ flows through each part of the circuit.
Answer (Detailed Solution Below)
Faraday's Law Question 2 Detailed Solution
Concept:
In a magnetic circuit, magnetic flux (\( \phi \)) behaves similarly to electric current in an electrical circuit. In a series magnetic circuit, all the magnetic components (like cores and air gaps) are arranged in series, and the same flux flows through each part, regardless of the varying reluctance of the individual sections.
Key Principle:
Just as current remains the same in a series electrical circuit, magnetic flux remains constant in a series magnetic circuit.
Evaluation of Options:
Option 1: the same – Correct
Same flux flows through all elements in a series magnetic circuit.
Option 2: different – Incorrect
Flux would differ only in parallel magnetic paths, not in series.
Option 3: zero – Incorrect
Flux exists as long as there is magnetomotive force (mmf).
Option 4: infinite – Incorrect
Infinite flux is not physically possible.
Faraday's Law Question 3:
According to Lenz’s law, what does the secondary current in a transformer produce?
Answer (Detailed Solution Below)
Faraday's Law Question 3 Detailed Solution
Concept:
According to Lenz’s Law, the direction of the induced current is always such that it opposes the cause producing it. In a transformer, when current flows in the secondary winding, it generates a magnetic field that opposes the magnetic field of the primary coil.
This opposition is what maintains energy conservation and proper transformer action. The effect of this opposing magnetic field is referred to as a demagnetizing effect.
Faraday's Law Question 4:
A coil of 100 turns is wound on a magnetic circuit of reluctance 1000 AT/mWb. The current of 1A flowing in the coil is reversed in 10 ms. The average EMF induced in the coil is ________ V.
Answer (Detailed Solution Below)
Faraday's Law Question 4 Detailed Solution
Concept
The average EMF induced in the coil is given by:
\(E=-N{Δ ϕ \over Δ t}\)
The magnetic flux is given by:
\(ϕ = {NI\over R}\)
where, E = EMF
N = No. of turns
Δϕ = Change in flux
Δt = Change in time
I = Current
R = Reluctance
Calculation
Given, N = 100
I = 1 A
R = 1000 AT/Wb
When the current reverses, the flux changes from Wb to Wb.
The change in flux is given by:
Δϕ = ϕfinal - ϕinitial
Δϕ = (−0.1) − (0.1) = −0.2 Wb
\(E=-(100)× {-0.2 \over 10× 10^{-3}}\)
E = 100 × 20 × 10-3 V
E = 2 V
Faraday's Law Question 5:
Which factor does NOT affect the magnitude of motional EMF in a conductor?
Answer (Detailed Solution Below)
Faraday's Law Question 5 Detailed Solution
Explanation:
Motional EMF in a Conductor
Definition: Motional EMF (Electromotive Force) is the voltage generated across a conductor when it moves through a magnetic field. This phenomenon is a direct consequence of Faraday's Law of Electromagnetic Induction, which states that a change in magnetic flux through a circuit induces an EMF in the circuit.
Working Principle: The principle behind motional EMF can be understood through the Lorentz force. When a conductor moves through a magnetic field, the free charge carriers (such as electrons) within the conductor experience a force due to the magnetic field. This force causes the charge carriers to accumulate on one end of the conductor, creating a potential difference (voltage) across the conductor. The magnitude of the motional EMF (ε) is given by the equation:
ε = B × L × v × sin(θ)
where:
- B is the magnetic field strength.
- L is the length of the conductor within the magnetic field.
- v is the velocity of the conductor.
- θ is the angle between the velocity of the conductor and the magnetic field.
The correct option is: The resistance of the conductor
Top Faraday's Law MCQ Objective Questions
If the conductor is stationary and the field is changing (varying), then emf induced in it. Such an emf is known as:
Answer (Detailed Solution Below)
Faraday's Law Question 6 Detailed Solution
Download Solution PDFDynamically 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?
Answer (Detailed Solution Below)
Faraday's Law Question 7 Detailed Solution
Download Solution PDFFaraday'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:
- By moving magnet
- By moving the coil
- By rotating the coil relative to a magnetic field
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:
\({\rm{E\;}} = {\rm{\;N\;}}\left( {\frac{{{\rm{d\Phi }}}}{{{\rm{dt}}}}} \right){\rm{Volts}}\)
According to Faraday's law, the voltage v induced in the coil with N turns and magnetic flux ϕ is:
Answer (Detailed Solution Below)
Faraday's Law Question 8 Detailed Solution
Download Solution PDFFaraday'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.
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.
Answer (Detailed Solution Below)
Faraday's Law Question 9 Detailed Solution
Download Solution PDFThe correct answer is option 3): 1250 V
Concept:
The Inductance of the coil is given by
L = \(N \phi \over I\) Henry
EMF . induced E = L\(di \over dt\) V
Calculation:
L = \(1000 ×0.25 × 10^{-3}\over 2\)
= 0.125
E = 0.125× \((10 -0) \over 1 \times 10 ^{-3}\)
(Where current changes from 10A to 0 A)
= 1250 V
“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?
Answer (Detailed Solution Below)
Faraday's Law Question 10 Detailed Solution
Download Solution PDFExplanation:
- Faraday’s first law states that whenever there is a change in the magnetic flux linked with a coil or a conductor, an electromotive force (EMF) is induced in the coil. This law describes the fundamental principle of electromagnetic induction, stating that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux.
- In the given statement, it describes the generation of EMF when a conductor or coil moves in a magnetic field, causing a change in the magnetic flux linked with the conductor.
- This change in flux induces an EMF in the conductor, in accordance with Faraday’s first law.
- Hence, the statement aligns with Faraday’s first law of electromagnetic induction
The direction of induced e.m.f. can be founded by
Answer (Detailed Solution Below)
Faraday's Law Question 11 Detailed Solution
Download Solution PDFCONCEPT:
Lenz's Law:
- According to this law, the direction of induced emf or current in a circuit is such as to oppose the cause that produces it.
- This law gives the direction of induced emf/induced current.
- This law is based upon the law of conservation of energy.
EXPLANATION:
- Laplace's law indicates that the tension on the wall of a sphere is the product of the pressure times the radius of the chamber and the tension is inversely related to the thickness of the wall. Therefore the option 1 is incorrect.
- According to Lenz's law, the direction of induced emf or current in a circuit is such as to oppose the cause that produces it. Therefore the option 2 is correct.
- Fleming's right-hand rule shows the direction of induced current but it gives no relation between the direction of induced emf or current in a circuit is such as to oppose the cause that produces it. Therefore the option 3 is incorrect.
- This law is also known as loop rule or voltage law (KVL) and according to it “the algebraic sum of the changes in potential in a complete traversal of a mesh (closed-loop) is zero”, i.e. Σ V = 0. Therefore the option 3 is incorrect.
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
Answer (Detailed Solution Below)
Faraday's Law Question 12 Detailed Solution
Download Solution PDFFaraday’s first law:
- Faraday’s first law of electromagnetic induction 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:
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:
- By moving a magnet towards or away from the coil.
- By moving the coil into or out of the magnetic field.
- By changing the area of a coil placed in the magnetic field.
- By rotating the coil relative to the magnet.
Faraday’s law of electromagnetic induction is mathematically described by which one of the following equations?
Answer (Detailed Solution Below)
Faraday's Law Question 13 Detailed Solution
Download Solution PDFFaraday’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:
\(\mathop \oint \nolimits_c \overset{\rightharpoonup}{E} .d\overset{\rightharpoonup}{l} = - \frac{{\partial \phi }}{{\partial t}} = - \frac{\partial }{{dt}}\mathop \smallint \nolimits_s \overset{\rightharpoonup}{B} .d\overset{\rightharpoonup}{s}\)
\( \mathop{\int }_{S}\left( \nabla \times \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {E} \right).d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {s}=-\int \frac{\partial B}{\partial t}.d\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {s}\)
\(\nabla \times \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {E}=-\frac{\partial B}{\partial t}\)
If the magnetic flux through each turn of the coil consisting of 200 turns is (t2 - 3t) milli-Webers, where t is in seconds, then the induced emf in the coil at t = 4 sec is
Answer (Detailed Solution Below)
Faraday's Law Question 14 Detailed Solution
Download Solution PDFConcept:
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 = (t2 – 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
A dielectric is subjected to an alternating electric field. The dielectric losses are proportional to:
Answer (Detailed Solution Below)
Faraday's Law Question 15 Detailed Solution
Download Solution PDFConcept:
- One of the important properties of the dielectric material is its permittivity. Permittivity ϵ is the measure of the ability of a material to be polarized by an electric field.
- ϵ is complex and is frequency dependent. The imaginary part corresponds to a phase shift of polarization relative to “E” and leads to the attenuation of EM waves passing through the medium.
- When a dielectric is subjected to an alternating electric field then, the dielectric loss will be;
\(W\left( t \right)=\frac{1}{2}\omega {{\epsilon }_{0}}{{\epsilon }_{\text"{r{}}}}~E_{0}^{2}~W/{{m}^{3}}\)
Where, ω = Angular frequency
ϵ0 = Absolute permittivity
ϵr“ = Imaginary part of complex relative permittivily
E0 = Peak Voltage.