Magnetic Force MCQ Quiz - Objective Question with Answer for Magnetic Force - Download Free PDF

The correct answer is: 4) The magnetic field lines spread out and become weaker.

Explanation:

• Magnetic fringing occurs at the ends of a magnetic circuit because:
• Magnetic field lines encounter lower reluctance in air compared to the core material, causing them to spread outward (fringe) rather than staying confined.
• This spreading leads to a weaker magnetic field near the edges, as some flux "leaks" instead of following the intended path.

Why Not the Other Options?

1. The MMF is not constant → MMF (magnetomotive force) depends on the current and turns; fringing occurs even with constant MMF.
2. The reluctance of the material increases → Reluctance is a property of the material and doesn’t inherently cause fringing.
3. The magnetic poles are not well-defined → While poles exist, fringing is due to flux spreading, not pole definition.

Concept:

Magnetic Force on a Moving Charge:

When a charged particle moves in a uniform magnetic field, it experiences a force given by the Lorentz force equation :

F = q (v × B)

where:

q = Charge of the particle

v = Velocity of the particle

B = Magnetic field

× = Vector cross-product operation

In the second case, the charged particle moves along the z-axis with velocity v₂ = 10⁶ m/s , experiencing a force F₂ in the y-direction .

Calculation:

Given:

Magnetic field, B = (2 î) T

Velocity in the second case, v₂ = 10⁸ m/s (along the z-axis)

The magnetic force is given by:

F₂ = B₀ q v₂ sin 90°

Since the angle between B and v₂ is 90° , we substitute the given values:

F₂ = (2) (10^-6) (10⁸)

F₂ = 200 N

Concept:

Magnetic Force on a Moving Charge:

When a charged particle moves in a uniform magnetic field, it experiences a force given by the Lorentz force equation :

F = q (v × B)

where:

q = Charge of the particle

v = Velocity of the particle

B = Magnetic field

× = Vector cross-product operation

From the problem, we are given two cases where the particle moves with different velocities and experiences different forces. By using the cross-product rule and solving for B , we can determine the magnitude of the magnetic field.

Calculation:

Given:

Charge, q = 10 μC = 10^-5 C

Velocity in the first case, v₁ = 10⁶ m/s at 30° in the x-y plane

Force experienced in the first case, F₁ = 10 N along the negative z-axis

Using the cross-product equation:

(-10) k̂ = (10^-5) [(10⁶ √3/ 2) î + (10⁶ / 2) ĵ] × (B₀ î)

Expanding the cross-product:

- 5B₀ k̂ = -10 k̂

Solving for B₀:

B₀ = 2 T

Ans.(2)

Sol.

Force between two parallel current carrying conductors is attractive, if they carry current in same direction and repulsive, if they carry current in opposite direction. So, the branch AD is attracted to the long wire, while the branch BC is repelled by it. Since the force is inversely proportional to the distance between the two wires, the force of attraction is more than the force of repulsion. Hence there is a net force attracting the loop towards the wire and the loop will move towards the wire

We know,

\(\dfrac{hc}{\lambda}-\phi=KE_{max}\)

\(\dfrac{6.62\times 10^{-34} \times 3\times 10^{8}}{180\times 10^{-9}}- 2\times 1.6\times 10^{-19}=KE_{max}\)

\(\dfrac{19.86\times 10^{-17}}{180}-3.2\times 10^{-19}\)

\(11.03\times 10^{-19}-3.2\times 10^{-19}=7.83\times 10^{-19}= KE_{max}\)

Now,

\(R=\dfrac{\sqrt{2\times m\times KE}}{qB}=\dfrac{\sqrt{2\times 9.1\times 10^{-31}\times 7.83\times 10^{-19}}}{1.6\times 10^{-19}\times 5\times 10^{-5}}\)

\(=\dfrac{\sqrt{142.506\times 10^{-50}}}{8\times 10^{-24}}= \dfrac{11.937 \times 10^{-1}}{8}\)

\(=1.4921 \times 10^{-1}=0.1492\ m\)

\(\textrm{Radius}= 149.2 \times 10^{-3}\textrm{ metres}\)

Concept:

Magnetic Field Strength (H): the amount of magnetizing force required to create a certain field density in certain magnetic material per unit length.

\(H=\frac{NI}{L}\)

The intensity of Magnetization (I): It is induced pole strength developed per unit area inside the magnetic material.

The net Magnetic Field Density (Bnet) inside the magnetic material is due to:

• Internal factor (I)
• External factor (H)
   

∴ Bnet ∝  (H + I)

Bnet = μ0(H + I) …. (1)

Where μ0 is absolute permeability.

Note: More external factor (H) causes more internal factor (I).

∴ I ∝  H

I = KH …. (2)

And K is the susceptibility of magnetic material.

From equation (1) and equation (2):

Bnet = μ0(H + KH)

Bnet = μ0H(1 + K) …. (3)

Dividing equation (3) by H on both side

\(\frac{{{B_{net}}}}{H} = \frac{{{μ _0}H\left( {1 + K} \right)}}{H} \)

or, μ0μr = μ0(1 + K)

∴ μ_r = (1 + K) .... (4)

From equation (3) and (4)

Bnet = μ0μ_rH

Calculation:

Given Magnetic Circuit,

N = 100
I = 5 A
L = 2πr = 2π × 5 × 10^-2 m

From above concept,

\(H=\frac{NI}{L}=\frac{100× 5}{10π × 10^{-2}}=\frac{5000}{π}\)

We know that,

Bnet = μ0μrH

And, μ_r = 1000

\(B_{net}=4\pi \times 10^{-7}\times 1000\times \frac{5000}{\pi}=2\ T\)

Magnetic pole strength:

• It is a measure of the force exerted by one face of a magnet on a face of another magnet when both magnets are represented by equal and opposite poles.
• Symbol: m.

Units:

• There are two possible units for magnetic pole strength in SI units, depending on how the pole force is described.
• If you describe this as force per unit field B, then the SI unit is the ampere-meter (Am).
•  It can also be defined as the force per field of unit H, in this case, the unit SI is the weber (Wb).
• Unit of magnetic pole strength is Am or Wb.

Magnetic field intensity (H):

• Magnetic field strength refers to the ratio of the MMF which is required to create a certain Flux Density (B) within a certain material per unit length of that material. Some experts also call is as the magnetic field intensity.
• Furthermore, the magnetic flux refers to the total number of magnetic field lines that penetrate an area. Furthermore, the magnetic flux density tends to diminish with increasing distance from a straight current-carrying wire or a straight line which connects a pair of magnetic poles around which the magnetic field is stable.
• Magnetic field strength refers to a physical quantity that is used as one of the basic measures of the intensity of the magnetic field. The unit of magnetic field strength happens to be ampere per meter or A/m.
•  

B = μ H

B in terms of force is expressed according to Lorentz force equation as

B = \(\frac{F}{{qv\;sin\theta }}\)

Where F is force in newtons (N)

             q is charge

             v is velocity.

Therefore H = N / Am

                   H = N / Wb. 

MMF Waveform by single-coil:

The following diagram shows the stator and rotor of the machine having one coil on rotor a and a'.

For calculating MMF we have to draw the waveform, the waveform is as follows,

The waveform shows the magnetic field direction for the coil. The magnetic field is anticlockwise for dot i.e; a and Clockwise for cross i.e; a'.

As we know that a magnetic field is created then poles are also formed.

By using ampere law,

Ampere’s circuit law:

It states that the line integral of the tangential component of ''H'' around a closed path is the same as the net current “Ienc” enclosed by the path.

i.e.\(\oint \vec H \cdot d\ell = {I_{enc}}\)   ......(1)

For N no. of turns the current enclosed in NI. 

The H is equal to 2 Hg.

Here g is an air gap length.

The 2 is added because the air gap comes in the picture twice. 

So, the equation (1) becomes,

2 Hg =  NI

\(Hg = \frac{NI}{2}\)

Reluctance is maximum in air gap that's why we take the dot product of air gap and avoiding in iron part.

Waveform 2 shows the square wave of MMF. 

the magnitude of this square wave is \(\frac{NI}{2}\)

The square wave is symmetric about zero.

For calculating fundamental components, we take the Fourier series of the square waves.

The Fourier series of the square wave is,

\(\displaystyle\sum_{n=1,2,3,...}^{\infty}\frac{-4F_p}{n\pi} cosn\alpha\)

We take the -ve sign because the waveform is started from the -ve value.

The fundamental components are,

Put n = 1

\(F_1=\frac{-4F_p}{\pi} cos\alpha\)

\(F_1 =( \frac{-4}{\pi})(\frac{NI}{2}) cos\alpha\)

Fundamental peak value,

\(F_{1p}=\frac{4}{\pi}(\frac{NI}{2})\)

\(F_{1p}=\frac{2NI}{\pi}\)

Given that I = 1.

The fundamental peak component of MMF is,

\(F_{1P} = (\frac{2}{\pi})N\)

The correct answer is option 2):(100)

Concept:

Maxwell Unit:

A maxwell is a non-SI unit.

One maxwell is the total flux across a surface of one square centimetre perpendicular to a magnetic field of strength one gauss.

1 Line is equivalent to 1 maxwell 

100 maxwells =  100 magnetic line

Additional Information 

1 maxwell = 1 gauss × cm² .... (1)

Since gauss is a CGS unit and it is given by,

1 gauss = 10^_-4 Tesla And, 1 cm = 10^-2 m

From equation (1),

1 maxwell = 10^-4 Tesla × 10^-4 m² or,

1 maxwell = 10^-4 wb/m2 × 10^-4 m² (T = wb/m²)

Magnetomotive force (MMF):

The current flowing in an electric circuit is due to the existence of electromotive force similarly magnetomotive force (MMF) is required to drive the magnetic flux in the magnetic circuit. The magnetic pressure, which sets up the magnetic flux in a magnetic circuit is called Magnetomotive Force.

The strength of MMF is equal to the product of the current and no. of turns of the coil

MMF can be expressed as

MMF = N I = (Flux) x (Reluctance)

The SI unit of MMF is ampere-turn (AT).

The Reluctance (S) is given as,

\(S=\frac{l}{\mu_0\mu_rA}\)

Calculation:

The Airgap length (l) = 0.2 mm = 0.2 × 10³ m

Cross-section area (A) = 1 cm2 = 10^-4 m²

Reluctance of airgap will be

\({S} = \frac{{{l}}}{{{\mu _o}A}} = \frac{{0.2 × {{10}^{ - 3}}}}{{4\pi × {{10}^{ - 7}} × 1 × {{10}^{ - 4}}}}=\frac{2}{4\pi \times 10^{-7}}\)

MMF = Flux × reluctance

\(MMF=100\times 10^{-6}\times \frac{2}{4\pi \times 10^{-7}}=\frac{500}{\pi}\ AT\)

Concept:

The magneto motive force ( MMF ) for a coil having N turns, carrying current I is given by

MMF = N × I  and is responsible for causing the Flux.

The direction of Flux is given by Flemings Right hand curl rule.

Application:

Given:

N_a = 300, I_a = 1.5 A, N_b = 600, I_b = 4 A, N_c = 600, I_c = 3 A

Let us assume direction of flux in upward direction be +ve and downward direction be -ve

For Coil A, MMF_a = N_a I_a = 300 × 1.5 = 450 AT ( + )

For coil B, MMF_b = N_b I_b = 600 × 4 = 2400 AT ( + )

For coil C, MMF_c = N_c I_c = 600 × 3 = 1800 AT ( - )

Net MMF = 450 + 2400 - 1800 = 1050 AT

Note: The direction of flux for coil a and coil b are in same direction and in opposite direction for coil c.

Concept:

Electrostatic force: It is the electric force on a static charge (Q) in a conductor due to an Electric field (E) and it is given as,

F_e = EQ

Magnetostatic force: It is the Magnetic force on a charge moving with a velocity (V) in a conductor due to Magnetic field (B) and it is given as,

F_m = Q (V × B)

Lorentz force:

If a moving charge is present in both electric field and magnetic field then the force on a charge in a conductor is known as Lorentz force.

F = F_e + F_m

F = EQ + Q (V × B)

This equation is known as the Lorentz force equation.

Note: All bold letters are vectors.

So, the electromagnetic wave experiences the Lorentz force which is the combination of the electrostatic force and magnetostatic force.

Magnetic effect of current:

• The magnetic effect of electric current was discovered by H.C. Oersted in 1820. 
•  He observed that the flow of electric current through a conductor produces a magnetic field around it.

The magnetic effect of current was proved by an experiment which was as under:

1. Initially, the magnetic needle was put on the axis of the magnetic meridian. When a current flows through the circuit, the needle got deflected in the direction of the electric current.
2. And when the direction of the electric current was reversed, the needle got deflected in the opposite direction.
3. This proved that the magnetic effect was produced by the electric current and the electric field is a source of the magnetic field and vice-versa.

Concept:

Magnetic field strength or field intensity (H) is the amount of magnetizing force.

Magnetic flux density (B) is the amount of magnetic force induced on the given body due to the magnetizing force H.

The relation between B and H is,

B = μH

Where, 

μ = μ₀ μ_r =  Permeability of the material

μ₀ = Absolute permeability = 4π x 10^-7 H/m

μ_r = relative permeability 

Calculation:

Given-

H = 800 AT/m , μ_r = 1 (∵ for air)

So that flux density for given magnetising force will be

B = 4π x 10-7 x 800 = 1.0053 x 10^-3

B ≈ 1 mWb/m²

If magnetic field lines intersect each other, then at the intersection point there will be two directions of the same field which is not possible. 

Hence, magnetic field lines do not cross or intersect each other.

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Additional InformationMagnetic field and magnetic lines of force: It is the space around a magnetic pole or magnet or current-carrying wire within which its magnetic effect can be experienced is defined as a magnetic field.

• The magnetic field can be represented with the help of a set of lines or curves called magnetic lines of force or magnetic field lines.

Properties of magnetic field line:

1. The magnetic field line is directed from the north pole to the south pole outside and south to the north inside the magnet.
2. Magnetic field lines are closed and continuous.
3. Magnetic field lines are more crowded near poles which shows that the strength of the magnetic field is maximum at its poles.
4. Magnetic field lines never intersect with each other.