SSC JE Electrical Previous Year Question Paper 2018-SET 5

Ques.21. Which one of the following is the CORRECT expression for Biot-Savart law?

$\begin{array}{l}1.\oint {B.dl = {\mu _o}} \sum 1\\\\2.{\Phi _E} = \dfrac{q}{{{\varepsilon _o}}}\\\\3.dB \propto \dfrac{{K.ids\sin \theta }}{{{r^2}}}\\\\4.dB = \dfrac{{idl\sin \theta }}{{{r^2}}}\end{array}$

Biot-Savart Law

The relationship between magnetism and electricity was discovered in 1819 when, during a lecture demonstration, Hans Christian Oersted found that an electric current in a wire deflected a nearby compass needle. In the 1820’s, further connections between electricity and magnetism were demonstrated independently by Faraday and Joseph Henry (1797-1878). They showed that an electric current can be produced in a circuit either by moving a magnet near the circuit or by changing the current in a nearby circuit. These observations demonstrate that a changing magnetic field creates an electric field. Years later, theoretical work by Maxwell showed that the reverse is also true: a changing electric field creates a magnetic field. In general, then, the source of a magnetic field is a moving electric charge.

Shortly after Oersted’s discovery, Jean-Baptiste Biot (1774-1862) and Felix Savart (1791-1841) performed quantitative experiments on the force exerted by an electric current on a nearby magnet. From their experimental results, Biot and Savart arrived at a mathematical expression that gives the magnetic field at some point in space in terms Or the current that produces the field. 

Biot Savart law

  • That expression is based on the following experimental observations for the magnetic field dB at a point P associated with a length element ds of a wire carrying a steady current I
  • The vector dB is perpendicular both to ds (which points in the direction of the current) and to the unit vector r directed from ds toward P.
  • The magnitude of dB is inversely proportional to r2, where r is the distance from ds to P.
  • The magnitude of dB is proportional to the current I and to the magnitude ds of the length element ds.
  • The magnitude of dB is proportional to sinθ, where θ is the angle between the vector ds and r.

These observations are summarized in the mathematical expression known today as the Biot-Savart law:

$dB \propto \frac{{ids\sin \theta }}{{{r^2}}}$

 

Ques.22. Which one of the following statements is TRUE about the magnetic lines of force?

  1. The magnetic lines of force travel from South pole to North pole outside the magnet
  2. The magnetic lines of force travel from North pole to South pole inside the magnet
  3. Magnetic lines of force never form a closed path
  4. Two magnetic lines of  force do not cut each other✓

The space surrounding a bar magnet/magnetic needle, in which its influence in the form of magnetic force can be detected, is called the magnetic field.

The curved lines around a bar magnet/magnetic needle, along which a freely suspended north pole will move in a magnetic field, are called the magnetic line of force or field line of force.

Magnetic line of force

Characteristics of magnetic field lines.

  • Magnetic lines of force are continuous and will always form closed loops. They are closed continuous curves, which originate from the north pole and end at the south-pole, outside the bar magnet. Within the magnet, they run from south to north
  • Magnetic lines of force will never cross one another. Two magnets placed near each other have separate magnetic fields which occupy an area common to both. One might gather from this that the lines of force cross or intersect. But this does not happen; lines of force never cross. When like poles face each other, the lines of force of each field remain separate entities, but -each field becomes distorted. When unlike poles face each other, the lines of force of each field interact with the other and produce a strong resultant field. 
  • Parallel magnetic lines of force traveling the same direction repel one another. Parallel magnetic lines of force traveling in opposite directions tend to unite with each other and form into single lines traveling in a direction determined by the magnetic poles creating the lines of force.
  • Magnetic lines of force never intersect each other:- Two lines of force never intersect each other, they did so, there would have been two tangents at the point of the intersection, that is two directions of the magnetic field at one point which is not possible
  •  Magnetic lines of force pass through all materials, both magnetic and nonmagnetic. There is no known insulator for magnetic lines of force. It has been found that flux lines will pass through all materials. Thus, most material all, except for magnetic materials, has no effect on magnetic fields. Conductors, insulators, air, or even vacuum do not affect magnetic fields. However, they will go through some materials more easily Ban others. This fact makes it possible to concentrate flux lines where they are used or to bypass them around an area or instrument.
  • Magnetic lines of force tend to shorten themselves. Another important behavior of magnetic lines of force is that each magnetic line behaves as though it were a stretched rubber band that if given the opportunity, would contract. This explains why unlike poles attract each other. The lines of magnetic force passing through the magnet behave as though they shrink, thus pulling the magnets towards each other.

 

Ques.23. Which one of the following materials is considered a non-magnetic material?

  1. Diamagnetic material
  2. Ferromagnetic material
  3. Ferrimagnetic material
  4. Anti-ferrimagnetic

The magnetic materials can be classified on the basis of magnetic property namely relative permeability μr. In general, a material is said to be non-magnetic if the value of μr is less than 1 or approximately equal to 1. While the material is said to be magnetic if the value of μr is greater than or equal to 1.

Generally, magnetic materials are classified into three major parts namely diamagnetic, paramagnetic and ferromagnetic. If a value of μis slightly less than unity then it is a diamagnetic material (μ< 1).

If the value of μr is slightly greater than unity, then it is paramagnetic material (μr ≥ 1). If the value of μis very large than unity (μr>>1), then it is the ferromagnetic material.

Diamagnetic Material

Diamagnetic materials are materials with relative permeabilities slightly smaller than 1 (μr < 1). This class includes important materials such as mercury, gold, silver, copper, lead, silicon, and water. The relative permeability of most diamagnetic materials varies between 0.9999 and 0.99999 (susceptibility varies between (-10-5 and -104), and for most applications, they may be assumed to be nonmagnetic.

An interesting aspect of diamagnetism is the fact that the magnetic flux density inside the diamagnetic material is lower than the external magnetic field. If we place a piece of diamagnetic material over a permanent magnet, the magnet will repel the diamagnetic material, as shown in Figure. 

diamagnetic sample

Since the magnet and the equivalent magnetic field (due to the magnetization of the diamagnet material) oppose each other, the diamagnetic material is always repelled from the magnetic field in the same way that two magnets repel each other when their magnetic flux densities oppose each other. However, this force is extremely small for diamagnetic materials, except superconductors, in which it is very large. This repulsion is the reason why a permanent magnet floats above a superconducting material.

 

Ques.24. On which of the following parameters the eddy current loss occurring in material does not depend?

  1. Magnetic flux Density
  2. The frequency of variation of flux
  3. Susceptibility
  4. The volume of the material

Eddy’s current Loss.

Eddy current losses occur because the iron core of the armature is a conductor revolving in a magnetic field. This sets up an emf across portions of the core, causing currents to flow within the core. These currents heat the core and, if they become excessive, may damage the windings.

Eddy current losses = Ke × Bm2 × f2 × V ×t2

Where 
Ke = Eddy current constant 
t = thickness of the core
V = Volume of material 
Bm = Maximum flux density
f = frequency 

Hence the eddy’s current losses do not depend on the Susceptibility of the material.

 

Ques.25. Determine the flux (in Wb) through a coil when the reluctance of the coil is 4 Amp-turns/Wb and the produced MMF is 48 Amp-turns

  1. 10
  2. 12
  3. 14
  4. 16

Similar to the resistance characteristic in electricity, we have reluctance in magnetism which is the property of the substance that opposes the magnetic flux through it.

The reluctance of any part of a magnetic circuit may be defined as the ratio of the drop in magnetomotive force to the flux produced in that part of the circuit. It is measured in ampere-turns/Weber and is denoted by S.

Reluctance = m.m.f ⁄ flux

4 = 48 ⁄ Flux

Flux = 2 Wb

 

Ques.26. Determine the current through a coil (in A), if the coil has 140 turns and produces MMF of 14 Amp-turns.

  1. 0.6
  2. 0.3
  3. 0.1
  4. 0.2

Magnetomotive force (MMF): It is defined as the force that drives magnetic flux throng the magnetic circuit. In all practical magnetic circuits, this is provided using a current-carrying winding (coil) and is the product of the current and the number of turns in the winding. Its SI unit of measurement is the ampere.

 m.m.f Fm = N.I Ampere-turn

where N is the number of conductors (or turns) 

I is the current in amperes.

The unit of MMF is sometimes expressed as ‘ampere-turns’. However, since ‘turns’ have no dimensions, the Sl unit of MMF is the amp.

Given

Number of turns N = 140 turns

MMF = 14 Amp-turns

Current I = ?

14 = 140 × I

I = 0.1 A

 

Ques.27. Determine the magnetic field strength (in A/m) of a material when the intensity of magnetization of the material is 0.084 Amp/m and the magnetic susceptibility of the material is 0.0012.

  1. 70
  2. 700
  3. 0.7
  4. 0.07

The magnetic susceptibility expresses the responsiveness of a material to the applied magnetic field and can vary with the external applied magnetic field. It is the ratio of the intensity of the magnetization “M” to the magnetizing force “H”.

The symbol for magnetic susceptibility is χ and the formula is

χ = M/H

Where

χ =  Magnetic susceptibility = 0.0012

M = intensity of the magnetization =0.084 Amp/M

H = Magnetic field strength = ? Amp – m−1

∴  The intensity of the magnetization M is

 H = M ⁄ χ

H = 0.084 ⁄ 0.0012

H =70 Amp/m

 

Ques.28. Determine the coupling factor between two coils each having a self-inductance of 40 mH and the mutual inductance between them is 40 mH

  1. 2
  2. 0.5
  3. 1
  4. 0.75

The coupling coefficient K is the degree or fraction of magnetic coupling that occurs between the circuit.

K = M/√L1L2

where

K = coupling factor = ?

M = Mutual inductance = 40 mH

L1 = primary circuit self-Inductance = 40 mH

L2 = secondary circuit self-inductance = 40 mH

K = 40/√40 × 40

K = 1

 

Ques.29. Determine the eddy current loss (in W) in a material having eddy current coefficient of 1, the thickness of 0.03 m, and volume of 2 cubic meters which is kept in a magnetic field of the maximum flux density of 3 T and supplied by a frequency of 50 Hz.

  1. 35.5
  2. 30.75
  3. 25.5
  4. 40.5

Eddy current losses in the transformer is given by

Eddy current losses = Ke × Bm2 × f2 × V ×t2

Where 
Ke = Eddy current constant = 1
t = thickness of the core = 0.03 m
V = Volume of material = 2 m3
Bm = Maximum flux density = 3 T 
f = frequency = 50 Hz
Eddy current losses = ?

Now put the above data in the equation we get

ELoss= 1 × 32 × (50)2 × 0.032 × 2

ELoss = 3.75

Bm = 40.5 watt

 

Ques.30. Determine the magnitude of the magnetic field (in mT) at the center of a 50 cm long solenoid, if the solenoid has 300 turns and carries a current of 5 A

  1. 2.61
  2. 2.66
  3. 4.64
  4. 3.77

The magnetic flux density at the center of a solenoid is given as

B = μoNI ⁄ L

Where

B = Magnetic flux density = ? mT

N = Numbers of turns = 300 turn

I = Current = 5A

L = Length of the solenoid = 50 cm = 0.5 m

µo = permeability of free space = 4π × 10-7

B = (4π × 10-7 × 300 × 5) ⁄ 0.5

B = 3.77 mT

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