SSC JE Electrical Previous Year Question Paper 2018-SET 4|MES Electrical

Magnetic lines of force do not attract each other while traveling in the same direction.

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.

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 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 newer 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 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.

Permeability is a measure of how easy it is to establish the flux in a material. Ferromagnetic materials have high permeability and hence low Reluctance, while nonmagnetic materials have low permeability and high Reluctance.

Relative permeability is the ratio of magnetic permeability of the medium (µ) to the magnetic permeability of free space (µo) is defined as relative permeability (µ_r), i.e.

µ_r = µ/µ_o

The substances, which when placed in an external magnetizing field, get magnetized feebly in the direction of the magnetizing field are called paramagnetic. Examples of paramagnetic substances are Aluminium, antimony, platinum, manganese, sodium, chromium, copper chloride, liquid oxygen etc.

Paramagnetic materials possess a relative permeability µ_r is slightly larger than 1. One example of this type of material is aluminum, for which cur= 1.00000036. Therefore, as with the diamagnetic materials, we can consider the materials as having µ_r = 1 for most practical purposes. In general, the effect due to paramagnetism is negligible.

Magnetic Flux density, “B” is defined to be the amount of magnetic flux crossing per unit area perpendicular or at the right angle to the direction of the magnetic flux. Its unit is the Tesla and its symbol T. These quantities are related by the simple expression:

B = φ/A

If the total flux cutting through an area of one square metro, perpendicular to the magnetic field is one Weber, then the flux density is one weber per square meter or one tesla.

MAGNETIC FIELD INTENSITY

Magnetic field Intensity (H) is also called as Magnetic field Strength, Magnetic Intensity, Magnetic field, Magnetic Force, and Magnetization Force.

Magnetic Field Strength (H)  gives the quantitative measure of the strongness or weakness of the magnetic field.

Suppose that a current of I amperes flows through a coil of N turns wound on a toroid of length I meters. The MMF is the total current linked to the magnetic circuit i.e  IN ampere-turns.

If the magnetic circuit is homogeneous and of the uniform cross-sectional area, the MMF per meter length of the magnetic circuit is termed as the magneticfield strength, magnetic field intensity, or magnetizing force. It is represented by the symbol H and is measured in ampere-turns per meter (At/m).

$H = \dfrac{{NI}}{l}{\text{ AT/m}}$

Hence the magnetic field Intensity can be defined as the ratio of applied MMF to the length of the path that it acts over.

Note:- Magnetic field intensity, H, is independent of the medium. Its value depends only on the number of turns N and the current I flowing in the coil.

Magnetic Field Strength is equivalent to Voltage gradient in an Electrical Circuit.

The Average Induced EMF is given as

E = L.Δi ⁄ t

Where

E = Induced EMF = 16 V

L is the inductance of the coil =?

t = time = 0.10 sec

Δi is the change in current in A

Now change in current

Δi = 4 − (−4) = 8A (since the current is reversed)

Putting all the value in the equation

16 = (L × 8) ⁄ 0.10

E = 0.2 Volt

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 = 0.4 × 10⁻⁵.

M = intensity of the magnetization =? Amp/M

H = Magnetic field strength = 1800 Amp – m⁻¹

∴  The intensity of the magnetization M is

 M = H × χ

H = 1800 × 0.4 × 10⁻⁵

M = 0.0072 A/m

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 

F_m = N.I Ampere-turn

where N is the number of conductors (or turns) and 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 = 100 turns

Current I = 0.2

F_m = 100 × 0.2

F_m = 20 Amp-turn

Critical Magnetic Field

The magnetic field at which the superconducting property of the material is lost is known as the critical magnetic field. Its value depends upon the nature of the material and its temperature.

The temperature dependence of Hc may be given by the following

${H_{c(t)}} = {H_{c(0)}}\left[ {1 – \dfrac{{{T^2}}}{{T_C^2}}} \right]$

where

H_c(T) is a critical magnetic field at temperature T and H_c(0) at 0 K.

T_C = Critical temperature

Critical Current

The magnetic field at which the superconductivity of material gets lost may not be necessary due to an externally applied field. Critical Current is defined as ‘the maximum value of the current flowing through the superconductor at which the superconducting properly ceases’. It is denoted by l_c.

If a superconducting wire of radius R carries a current I, then using Ampere’s law.

Ic = 2.π.R.Hc

Now coming back to the question

For wire, the critical field Hc(0) = 6 × 10⁴ Amp/m

Critical Temperature Tc = 12 K

Diameter = 2mm = 2 × 10⁻³ m

The critical field at temperature  T = 8 K

$\begin{array}{l}{H_{c(t)}} = 6 \times {10^4}\left[ {1 – {{\left( {\dfrac{T}{{{T_c}}}} \right)}^2}} \right]\\\\{H_{c(t)}} = 6 \times {10^4}\left[ {1 – {{\left( {\dfrac{8}{{12}}} \right)}^2}} \right]\\\\{H_{c(t)}} = 3.33 \times {10^4}A/m\end{array}$

Hence the critical current is

Ic = 2.π.R.Hc = 3.14 × 2 × 10⁻³ × 3.33 × 10⁴

I_C = 209.5 Ampere

Relation Between Magnetic Flux Density and Field Intensity is given as

B=μ_oH

where μ_o is called permeability of free space or magnetic space constant. Its value is 4π × 10^-7 H/m,

B = 4π × 10^-7  × 2 × 10⁵ 

B = 0.251 Tesla

The average induced E.M.F of the coil is the ratio of change in flux linkage to the time taken

E = N .dφ/dt

Given

A = area = 200 cm² = 2 × 10⁻² m²

Field intensity  B = 30 T

Number of turns = 100 turns

Now Magnetic field intensity is given as

B = φ/A 

or

φ = B.A = 30 × 2 × 10⁻² 

φ = 0.6 Weber

Hence the time taken will be

E = N .dφ/dt

100 = 100.d0.6/dt

1 = 0.6/t

t = 0.6 Sec.