Electromagnetism MCQ Quiz - Objective Question with Answer for Electromagnetism - Download Free PDF

Explanation:

Force on a Current-Carrying Conductor in a Magnetic Field

Definition: When a current-carrying conductor is placed within a magnetic field, it experiences a force due to the interaction between the magnetic field and the electric current. This phenomenon is described by the Lorentz force law.

Formula: The force experienced by a current-carrying conductor in a magnetic field is given by the equation:

F = I × L × B × sin(θ)

Where:

• F is the force acting on the conductor.
• I is the current flowing through the conductor.
• L is the length of the conductor within the magnetic field.
• B is the magnetic flux density.
• θ is the angle between the direction of the magnetic field and the direction of the current.

In this context, we are specifically interested in the case where the conductor is parallel to the magnetic field. This means that the angle θ between the direction of the current and the magnetic field is 0 degrees (or 180 degrees if considering the opposite direction).

Correct Option Analysis:

Given that the conductor is parallel to the magnetic field, the angle θ is 0 degrees. The sine of 0 degrees is 0. Therefore, the force experienced by the conductor can be calculated as:

F = I × L × B × sin(0)

Since sin(0) = 0:

F = I × L × B × 0

F = 0

Thus, the force experienced by the current-carrying conductor when it is lying parallel to the magnetic field is 0. This is because the magnetic force is perpendicular to the direction of the magnetic field and the current. When these two are parallel, there is no perpendicular component, and thus no force is exerted.

The correct answer is therefore:

Option 4: 0

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: BIL

This option would be correct if the angle θ were 90 degrees, meaning the conductor is perpendicular to the magnetic field. In that case, sin(θ) would be 1, and the force would be maximized at F = BIL. However, this does not apply when the conductor is parallel to the field.

Option 2: BIL sin(θ)

This is the general formula for the force experienced by the conductor, and it is always correct. However, for the specific case where θ is 0 degrees (parallel), sin(θ) is 0, and thus the force is zero. This option is not incorrect but does not directly provide the specific answer for the given condition.

Option 3: HIL

This option is incorrect because it uses H (magnetic field intensity) instead of B (magnetic flux density). The correct parameter in the context of the Lorentz force law is B, not H.

Conclusion:

Understanding the relationship between a current-carrying conductor and the magnetic field is crucial for determining the resulting force. When the conductor is parallel to the magnetic field, no force is exerted on the conductor as the angle θ is 0 degrees. This leads to the conclusion that the force experienced by the conductor is zero. Thus, the correct option is Option 4.

Explanation:

To determine the magnitude of the electromotive force (emf) induced in the coil at a specific time, we need to use Faraday's Law of Electromagnetic Induction. This law states that the induced emf in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.

Given the flux linked with the coil as a function of time: ϕ(t) = (5t² + 4t + 3) Weber

To find the induced emf at t = 2 seconds, we need to differentiate the flux function with respect to time (t) and then evaluate it at t = 2 seconds.

Step-by-Step Solution:

Step 1: Differentiate the flux function ϕ(t) with respect to time (t).

Given: ϕ(t) = 5t² + 4t + 3

The derivative of ϕ(t) with respect to t is:

dϕ(t)/dt = d/dt (5t² + 4t + 3)

Using the power rule of differentiation, we get:

dϕ(t)/dt = 10t + 4

Step 2: Evaluate the derivative at t = 2 seconds.

Substitute t = 2 into the derivative:

dϕ(t)/dt |_t=2 = 10(2) + 4 = 20 + 4 = 24

Step 3: Apply Faraday's Law of Electromagnetic Induction.

The magnitude of the induced emf (ε) is given by:

ε = - dϕ(t)/dt

Since we are interested in the magnitude, we take the absolute value:

ε = |dϕ(t)/dt|

At t = 2 seconds:

ε = |24| = 24 V

Therefore, the magnitude of the emf induced in the coil at t = 2 seconds is 24 V.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 10 V

This option is incorrect. As calculated, the derivative of the flux function at t = 2 seconds yields 24, not 10. Therefore, the induced emf cannot be 10 V.

Option 3: 31 V

This option is incorrect. The calculation of the derivative at t = 2 seconds gives us 24, not 31. Thus, the induced emf cannot be 31 V.

Option 4: 28 V

This option is also incorrect. The correct induced emf at t = 2 seconds, as calculated, is 24 V, not 28 V.

Conclusion:

Understanding Faraday's Law of Electromagnetic Induction and applying it correctly to the given function of magnetic flux is crucial for determining the induced emf. By differentiating the flux function with respect to time and evaluating it at the specified instant, we can accurately calculate the magnitude of the induced emf. In this case, the correct answer is 24 V, making Option 2 the correct choice.

Permanent Magnets:

Permanent magnets are magnets with magnetic fields that do not dissipate under normal circumstances. They are made from hard ferromagnetic materials, which are resistant to becoming demagnetized.

Permanent magnets are made from a material that will inherit the properties of a strong magnetic field when exposed to it.

Properties:

Residual induction:

The residual induction is any magnetic induction that remains in a magnetic material after removal of an applied saturating magnetic field, measured in gauss or tesla. Residual induction is also known as magnetic remanence.

Coercivity:

• Coercivity (or the coercive field) is the property of a material to resist demagnetization due to the intensity of the material's magnetic field
• Coercivity is measured by the extent to which a demagnetizing field must be applied to reduce the material's magnetism to zero
• Permanent magnets are composed of materials with a high coercivity which retains their inherited magnetic fields under most conditions, unless intentionally demagnetized

Hysteresis loop:

• Wider hysteresis loops have high retentivity, coercivity, and saturation due to their larger hysteresis loop area
• These loops are typically found in hard magnetic materials
• Due to the size, these hysteresis loops have low initial permeability which leads to higher energy dissipation
• For these reasons, they are utilized in permanent magnets that have high resistance to demagnetization
• Demagnetization is more difficult to achieve in these wider hysteresis loops because there is a larger area to cover when reversing the hysteresis loop direction back to its original paramagnetic state

Conclusion:

Hysteresis Loop:

Consider an un-magnetized iron bar AB wound with N turns as shown in Fig. below.

The magnetising force H (= NI/l) produced by this solenoid can be changed by varying the current through the coil.

The double-pole, double-throw switch (DPDT) is used to reverse the direction of current through the coil.

We shall see that when the iron piece is subjected to a cycle of magnetisation, the resultant B-H curve traces a loop abcdefa called a hysteresis loop.

Step 1:

• When the current in the solenoid is zero,  then, B, H = 0.
• As H is increased,  the flux density (+ B) also increases until the point of maximum flux density (+ B_max) is reached.
• The material is saturated and beyond this point, the flux density will not increase regardless of any increase in current or magnetising force.
• Note that the B-H curve of the iron follows the path oa.
   

Step 2:

• If now H is gradually reduced, it is found that the flux density B does not decrease along the same line by which it had increased but follows the path ab.
• At point b, the magnetising force H is zero but flux density in the material has a  finite value + Br (= ob) called residual flux density.
• The power of retaining residual magnetism is called retentivity of the material.
   

Step 3:

• To demagnetise the iron piece (i.e. to remove the residual magnetism ob), the magnetising force H is reversed by reversing the current through the coil.
• When H is gradually increased in the reverse direction, the B-H curve follows the path bc so that when (H = oc), the residual magnetism is zero.
• The value of H (= oc) required to wipe out residual magnetism is known as coercive force (Hc).

Hysteresis loss:

The energy loss associated with hysteresis is proportional to the area of the hysteresis loop. As the area of the hysteresis loop for a specimen is found to be large, the hysteresis loss in this specimen is also large.

So, hysteresis loss can be reduced by using material of narrow hysteresis loop

Hence statement 1 is true and statement 2 is false.

Concept

A copper rod of length l is rotated about one end, perpendicular to the uniform magnetic field B with constant angular velocity ω.

The induced EMF is given by:

\(E={dϕ \over dt}\)

Also, ϕ = BA

\(E=B{dA \over dt}\)

where, \({d\phi \over dt}=\) Rate of change of flux

E = Induced EMF

B = Flux density

Explanation

Consider a copper rod of length l is rotated about one end, perpendicular to the uniform magnetic field B with constant angular velocity ω.

If in time 't', the rod turns by the angle 'θ', the area  generated by the rotation of the rod will be:

\(A=({1\over 2}l)\times(l\theta)\)

\(A={1\over 2}l^2\theta\)

So, the flux linked with the area generated by the rotation of the rod:

\(\phi=B({1\over 2}l^2\theta)\)

\(\phi=B({1\over 2}l^2\omega t)\)

The induced EMF is:

\(E={1\over 2}{d(Bl^2\omega t) \over dt}\)

\(E={{1} \over 2} (Bl^2\omega)\)

The correct answer is option 2): No induced voltage is developed

Concept:

• When the AC current flows through a coil emf will be induced given by 

E = -N \(d\phi \over dt\)

where 

N is the number of turns

\(d\phi \over dt\) is change in flux

• In a coil, if a DC current is passed, No induced voltage is developed
• Because the change in flux is zero. Simply the coil will act as a resistor.

The correct answer is option 2):(Soft iron)

Concept:

• A solenoid is a device comprised of a coil of wire, the housing and a moveable plunger (armature).
• The important feature of the electromagnet is it needs to be demagnetised immediately when the electrical current is turned off, 
• When an electrical current is introduced, a magnetic field forms around the coil which draws the plunger in. 
• A solenoid Transforms electrical energy into mechanical work.
• The core of solenoid is made of soft iron, as it quickly loses its magnetism when current is switched off.

Concept:

Fleming's left-hand rule:

• When we stretch the forefinger, middle finger, and the thumb of our left hand in such a way that they are mutually perpendicular to each other, if the forefinger indicates the direction of the magnetic field and the middle finger indicates the direction of current, then the thumb will indicate the direction of the force on the conductor.

Additional Information

Fleming's Right -hand rule: 

• if we extend the forefinger, middle finger, and the thumb of our right-hand perpendicular to each other as shown in the figure and the thumb pointing towards the conductor's motion and the forefinger pointing towards the magnetic field direction, the middle finger gives us the direction of the induced current flowing in the circuit.

Right-hand thumb rule:

• If we hold the current-carrying conductor in the right hand such that the thumb points in the direction of the current, then the fingers encircle the wire will show the direction of magnetic lines of force.

The correct answer is option 4):250 v

Concept:

Average induced emf is given by E =  -N \(d\phi \over dt\)      

Where N is the number of turns

dϕ is changing in flux

dt is changing in time

Calculation:

Given that, number of turns (N) = 500

Change in time (dt) = 4 ×  10^-3 s

Magnetic flux (ϕ) =  1 × 10^-3 Wb

Since the flux is reversed, it changes from     1 × 10-3  Wb to -   1 × 10-3  Wb, which is a change of  -2 × 10-3 

E = -500 × \(-2 \times 10 ^{-3} \over 4 \times 10^{-3}\)

= 250 V

• When a conductor is placed in a magnetic field with changing magnetic flux, induced currents are produced in the conductor. These currents are called eddy currents.
• They are called eddy currents as they look like eddies or whirlpools.
• These currents are also called Foucault's currents as they were discovered by Foucault.

Analogy of electric and magnetic circuits:

Whenever a current carrying conductor is placed in a magnetic field, the conductor experiences a force which is perpendicular to both the magnetic field and the direction of the current.

According to Fleming's left-hand rule, if the thumb, forefinger and middle finger of the left hand are stretched to be perpendicular to each other as shown in the figure, and if the forefinger represents the direction of the magnetic field, the middle finger represents the direction of current, then the thumb represents the direction of force.

• Whenever a current-carrying conductor is placed in a magnetic field, the conductor experiences a force which is perpendicular to both the magnetic field and the direction of the current.
• According to Fleming's left-hand rule, if the thumb, forefinger and middle finger of the left hand are stretched to be perpendicular and if the forefinger represents the direction of the magnetic field, the middle finger represents the direction of the current, then the thumb represents the direction of a force.
• According to Fleming's right-hand rule, if the forefinger, thumb, and the central finger of the right hand are kept perpendicular to each other, such that the thumb points in the direction of motion of the conductor and the forefinger points in the direction of the magnetic field, then the central finger points in the direction of the induced current.
• This rule is used to determine the direction of flow of induced current in a conductor that is moved inside a magnetic field in a direction perpendicular to the direction of the magnetic field, this can be done when the direction of motion of the conductor and the direction of a magnetic field is known.
• 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 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.

Concept –

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 law of conservation of energy.

Faraday's Laws of Electromagnetic Induction –

• Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit/coil changes an emf is produced in the circuit called induced emf.
• The induced emf persists only as long as there is change or cutting of flux.
• The induced emf is given by rate of change of magnetic flux linked with the circuit i.e.

\(e = - N\frac{{d{\rm{\Phi }}}}{{dt}}\)

Where e = induced emf, N = number of turns and Φ = magnetic flux

Negative sign indicates that induced emf (e) opposes the change of flux.

Fleming's right hand –

• This rule states that if we arrange the thumb, the centre finger, and the forefinger of the right hand at right angles to each other, so that the thumb points towards the direction of the magnetic force, the centre finger gives the direction of induced current and the forefinger points in the direction of magnetic field . 
• Fleming's right-hand rule shows the direction of induced current.

Explanation –

• 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. 
• Faraday's Laws of Electromagnetic Induction gives the magnitude of emf.
• Kirchhoff’s law is related to junction rule of current and loop rule of electrical circuit.
• 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. 

• Eddy currents (also called Foucault currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction.
• Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field.
• The eddy currents cause energy to be lost from the transformer as they heat up the core i.e. electrical energy is being wasted as unwanted heat energy.
• So that core is laminated to reduce eddy current to a minimum as they interfere with the efficient transfer of energy from the primary coil to the secondary one.