Magnetostatic Field MCQ Quiz - Objective Question with Answer for Magnetostatic Field - Download Free PDF

Explanation:

Artificial magnets are man-made magnets, specifically designed and manufactured to possess desired magnetic properties. These magnets are utilized in various applications, including electrical motors, transformers, sensors, and other devices that rely on magnetic fields for operation. Their efficiency, stability, and durability are critical factors in determining their suitability for specific applications.

Correct Option Analysis:

The correct option is:

Option 1: Ceramic Magnet

Ceramic magnets, also known as ferrite magnets, are the best-suited artificial magnets for use in electrical motors and transformers due to their high efficiency and stable magnetic field. These magnets are composed of a ceramic material that includes iron oxide combined with other elements such as barium or strontium. They are widely recognized for their excellent magnetic properties, cost-effectiveness, and versatility in various applications.

Key Features of Ceramic Magnets:

• High Stability: Ceramic magnets exhibit a stable magnetic field over time, making them ideal for applications where consistency is crucial, such as in electrical motors and transformers.
• Resistant to Demagnetization: These magnets are highly resistant to demagnetization, ensuring long-term reliability in demanding environments.
• Cost-Effective: Ceramic magnets are relatively inexpensive to produce, making them an economical choice for industrial applications.
• Wide Operating Temperature Range: They can operate effectively over a broad temperature range without significant loss of magnetic properties.
• Corrosion Resistance: Ceramic magnets are resistant to corrosion, allowing them to function efficiently in various environmental conditions.

The correct answer is  3) Soft magnetic material

Explanation:

• A soft magnetic material is easily magnetized when an external magnetic field is applied and loses its magnetism when the field is removed.

• It has low coercivity and low retentivity, making it ideal for applications like transformer cores and electromagnets where temporary magnetism is needed.

Additional Information

• 1) Hard magnetic material:
  Retains magnetism even after the external field is removed (used in permanent magnets).

• 2) Ferromagnetic material:
  A general term for materials (like iron, cobalt, nickel) that show strong magnetic properties, which can be soft or hard.

• 4) Permanent magnet:
  Made of hard magnetic material; keeps its magnetism permanently.

High Permeability in Magnetic Materials

Definition: Permeability is a property of a magnetic material that measures its ability to support the formation of a magnetic field within itself. High permeability indicates that the material allows magnetic field lines to pass through it more easily, making it an ideal choice for use in magnetic circuits.

Magnetic Circuit and Permeability:

In a magnetic circuit, magnetic flux is analogous to current in an electrical circuit, and reluctance is analogous to resistance. The relationship between these parameters can be expressed by the magnetic version of Ohm's Law:

Φ = MMF / Reluctance

Where:

• Φ is the magnetic flux
• MMF is the magnetomotive force
• Reluctance (R_m) is the opposition to the formation of magnetic flux, analogous to electrical resistance

The reluctance of a magnetic circuit is inversely proportional to the permeability of the material. That is:

R_m = l / (μ × A)

Where:

• l = Length of the magnetic path
• μ = Permeability of the material
• A = Cross-sectional area of the material

From this relationship, it is clear that as the permeability (μ) of a material increases, the reluctance (R_m) decreases. This means that the material offers less opposition to the magnetic flux, making it easier for the flux to pass through the material.

Correct Option Analysis:

The correct option is:

Option 1: Decreased reluctance

When a magnetic material has high permeability, its reluctance decreases. This is because reluctance is inversely proportional to permeability, as shown in the formula above. A material with high permeability allows magnetic flux to pass through it more readily, reducing the overall reluctance of the magnetic circuit. This property is particularly important in designing magnetic cores for transformers, inductors, and other electromagnetic devices, where minimizing reluctance is essential for efficient operation.

Explanation:

Magnetic Flux and Reluctance

Definition: Magnetic flux (Φ) is a measure of the total magnetic field passing through a given area. It is expressed in Weber (Wb). Reluctance (ℜ), on the other hand, is the opposition offered by a magnetic circuit to the flow of magnetic flux, analogous to resistance in an electrical circuit. Reluctance is given by the formula:

ℜ = l / (μ × A)

Where:

• l = Length of the magnetic path (in meters)
• μ = Permeability of the material (in Henry/meter)
• A = Cross-sectional area of the magnetic path (in square meters)

The relationship between the magnetomotive force (MMF), reluctance, and magnetic flux is given by:

Φ = MMF / ℜ

Where:

• Φ = Magnetic flux (in Weber)
• MMF = Magnetomotive force (in Ampere-turns)
• ℜ = Reluctance (in Ampere-turns per Weber)

Correct Option Analysis:

The correct option is:

Option 4: The flux will decrease.

If the length of the magnetic path is increased while keeping the cross-sectional area (A) and magnetomotive force (MMF) constant, the reluctance of the magnetic circuit will increase. This is because reluctance (ℜ) is directly proportional to the length of the magnetic path (l). As reluctance increases, the magnetic flux (Φ), which is inversely proportional to reluctance, will decrease. This can be mathematically expressed as:

Φ = MMF / ℜ

With a higher reluctance (ℜ) due to an increased length (l) of the magnetic path, the denominator in the above equation becomes larger, resulting in a smaller value of Φ. Thus, the magnetic flux will decrease

Concept:

The magnetic field intensity H due to an infinitely long straight current-carrying conductor at a distance r is given by:

\(H = \frac{I}{2\pi r} \text{ A/m}\)

Given:

• Current I = 10 A
• Distance between wires = 5 m
• Point P is 1 m away from the left wire and 4 m away from the right wire
• Currents are in opposite directions

Calculation:

Magnetic field at P due to the left wire:

H₁ = \(\frac{10}{2\pi \cdot 1} = \frac{10}{2\pi} = \frac{5}{\pi}\)A/m

Magnetic field at P due to the right wire:

H2 = \(\frac{10}{2\pi \cdot 4} = \frac{10}{8\pi} = \frac{5}{4\pi} \text{ A/m}\)

Since currents are in opposite directions, the magnetic fields will add up at point P (in the same direction due to the right-hand rule):

\(H = H_1 + H_2 = \frac{5}{\pi} + \frac{5}{4\pi} = \frac{20 + 5}{4\pi} = \frac{25}{4\pi} \text{ A/m}\)

Convert to match the options given (denominator \(8\pi\)):

\(H = \frac{25}{4\pi} = \frac{50}{8\pi} \text{ A/m}\)

Hence, the correct option is 1

CONCEPT:

• Magnetic field strength or magnetic field induction or flux density of the magnetic field is equal to the force experienced by a unit positive charge moving with unit velocity in a direction perpendicular to the magnetic field.
  • The SI unit of the magnetic field (B) is weber/meter2 (Wbm-2) or tesla.
• The CGS unit of B is gauss.

​1 gauss = 10-4 tesla.

EXPLANATION:

• From the above explanation, we can see that the relation between tesla and Weber/m2 is given by:

1 tesla = 1 Weber/m2

In an electric magnetic circuit, for establishing a magnetic field, energy must be spent, through no energy is required to maintain it.

Let us take on the example of exciting coils of electromagnetic as shown in the figure:

The energy supplied to it is spent in two ways:

• Part of it goes to meet I²R losses and is lost once for all.
• Part of it goes to create a flux and is solved in the form of the magnetic field as “potential energy” and is similar to the potential energy of a raised weight when a mass ‘M’ is raised through height ‘H”, the potential energy solved it is MgH.
• Work is done in raising the mass, but once the mass is raised to a certain height, no further expenditure of energy is required to maintain it at that position.
• This mechanical potential energy can be recovered to get electrical energy which is stored in the form of a magnetic field.

• Magnetic field strength is also called as the magnetic intensity. 
• The magnetic field is a region around a magnetic material or a moving electric charge within which the force of magnetism acts.
• Magnetic field strength arises from an external current and is not intrinsic to the material itself.
• It may be defined in terms of magnetic poles: one centimetre from a unit pole the field strength is one oersted.
• The magnetic field strength is defined by the unit of Oersted (Oe) or Ampere/metre (A/m). When it is defined by flux density, the units of Gauss (G) or Tesla (T) are used.

Concept:

Absolute Permeability(μ): Absolute permeability is related to the permeability of free space and is a constant value which is given as:

• μ0 = 4π × 10-7 H/m
• Its dimension is [M L T-2 A-2]
• The absolute permeability for other materials can be expressed relative to the permeability of free space as:

           μ = μ0μr

Where μr is the relative permeability which is a dimensionless quantity.

Additional Information

Relative Permeability(μr): Relative permeability for a magnetic material is defined as the ratio of absolute permeability to absolute permeability of air. It is a unitless quantity.

Susceptibility(K): It is the ratio of the intensity of magnetization (I) to the magnetic field strength(H). It is a unitless quantity.

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

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) cause 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

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

or, μ0μr = μ0(1 + K)

∴ μr = (1 + K)

Susceptibility (K) is normally considerd as unitless quantity.

Note: Sometimes the value of susceptibility is given in terms of H/m and denoted by (K').

And, K' = Kμ

∴ \({\mu _r} = 1 + \frac{K'}{{{\mu _0}}}\)

Magnetic field strength (B):

• Magnetic field strength refers to the ratio of the MMF which is required to create a certain Flux Density within a certain material per unit length of that material. Some experts also call is as the magnetic field intensity.
• Furthermore, 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 that 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.
• As the distance of a point from the magnet increases the magnetic flux density decreases and the magnetic field intensity decreases. 

​The magnetic intensity due to an isolated pole of strength mp at a distance (r) is:

\(B=\frac{\mu_om_p}{4\pi r^2}\)

Hence option (4) is the correct answer.

The inductance is given by:

\(L = \frac{{{μ }{N^2}A}}{l} \)

Where,

N = Number of turns

A = Cross-sectional area 

l = length 

μ = Permeability

Energy stored by the inductor is given by: 

\(E=\frac{1}{2}LI^2\)

Where, I = Current flowing through the inductor

Note that, Inductor stores energy in the form of magnetic field.

∴ Energy stored in a magnetic field of length l metre and of cross-section A sq-m is given by:

\(E=\frac{1}{2}LI^2\)

\(E=\frac{1}{2} \times {{μ A}\frac{N^2}{l}}\times{I^2}\) Joule

Concept:

Magnetic flux density for any current-carrying element is given by:

B = \(( {μ_o\over 4π } \times {I\over r })\times ϕ \)

where, B = Magnetic flux density

μ_o = absolute permeability

I = current flowing in current-carrying element

r = distance from current-carrying element to required point

ϕ = angle made by current-carrying element with respect to the required point

Explanation:

B_net = B₁ + B₂ + B₃

Magnetic flux densities B₁ and B₃ are equal to zero as the current flowing is equal and opposite in nature.

So, B_net will be due to circular loop only.

Hence, ϕ = 2π

Bnet =  B₂

B_net = \(( {μ_o\over 4π } \times {I\over r })\times 2\pi \)

Bnet = \( {μ_o\over 2 } {I\over r }\)

Fleming's Right-hand Rule: 

This rule shows the direction of induced current when a conductor attached to a circuit moves in a magnetic field. It can be used to determine the direction of current in a generator's windings.

Fleming’s left-hand Rule:

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.

In an electric motor, the electric current and magnetic field exist (which are the causes), and they lead to the force that creates the motion (which is the effect), and so the left-hand rule is used.

Right-hand thumb rule:

• The Right-hand thumb rule is used to determine the direction of magnetic field around a current carrying wire.
• This rule states that "when an electric current passes through a straight wire that is held by the right hand with the thumb pointing upwards and the fingers curling up the wire, the thumb points in the direction of the conventional current (from positive to negative), and the fingers point in the direction of the magnetic field".
• Below figure represents the direction of current and magnetic field through a straight current carrying conductor.

Concept:

The force between two long parallel conductors is given by:

\(\frac{F}{l} = \frac{{{\mu _0}}}{{2\pi }}\frac{{{I_1}{I_2}}}{d}\)

Where F is the force

l is the length

I1 and I2 are the currents flowing through the two conductors

d is the distance between the conductors

The force between two long parallel conductors is inversely proportional to the distance between the conductors.

The nature of force depends on the direction of current, i.e.

1) If the current flowing in both the wires is in the same direction, the two wires will attract each other.

2) If the current flowing in both the wires is in the opposite direction, the two wires will repel each other.

Calculation:

Given: I₁ = I₂ = 4 A, d = 6 mm = 6 × 10^-3 m, l = 0.6 m

The mutual force between the conductors will be:

\(F= \frac{{{\mu _0}}}{{2\pi }}\frac{{l\times{I_1}{I_2}}}{d}\)

\(F= \frac{{{\mu _0}}}{{2\pi }}\frac{{0.6\times{4}\times {4}}}{6\times 10^{-3}}\)

\(F= \frac{{{4\pi \times 10^{-7}}}}{{2\pi }}\frac{{0.6\times{4}\times {4}}}{6\times 10^{-3}}\)

Solving the above, we get:

F = 3.2 × 10-4 N

Since the current flowing in both the wires is in the opposite direction, the two will repel each other.

Notes:

Case 1: Two conductors are in parallel and this arrangement is connected in series with dc supply.

During this arrangement total current I from supply flows in two paths I1 for conductor 1) and I2 for conductor 2). Thus current in both the wire flow in some direction thus there would be an attractive force between these two conductors.

Case 2: Two conductors are in series & this arrangement is connected in series with dc supply.

During this arrangement, the total current I flows through the two conductors. Since they are connected in series connection, the same current flows in both conductors but the direction of the current will be in opposite direction. Thus there would exist repulsive force between these two conductors.

The correct answer is Soft Iron.

• Soft iron is selected for making the core of an electromagnet because the core is used in a solenoid for the production of the strongest magnetism.

Additional Information

•  The strongest continuous manmade magnetic field, 45 T, was produced by a hybrid device, consisting of a Bitter magnet inside a superconducting magnet.
  • The resistive magnet produces 33.5 T and the superconducting coil produces the remaining 11.5 T.
• The magnetic field is strongest at the centre and weakest between the two poles just outside the bar magnet.
  • The magnetic field lines are densest at the centre and least dense between the two poles just outside the bar magnet.
  • The intensity of the field is weakest near the equator where it is horizontal.
  • The magnetic field's intensity is measured in gauss.
  • The magnetic field has decreased in strength through recent years.