SSC JE Electrical Previous Year Question Paper 2018-SET1|SSC JE 2018

MAGNETIC FIELD INTENSITY

Magnetic field Intensity (H) is also called 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 a uniform cross-sectional area, the MMF per meter length of the magnetic circuit is termed 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 the Voltage gradient in an Electrical Circuit.

Given Resistance “R” = 80 Ω
Capacitance “C” = 0.01 mF
Inductance “L” = 2 mH = 2 × 10^-3

The bandwidth of the series RLC circuit is given as

B.W = R/L

B.W = 80 ⁄ (2 × 10^-3)

B.W = 40 Hz

Given

Line voltage V_L = 440 V

Phase current I_ph = 50 A

Phase angle φ = 45°

In star connection the line current and phase current are equal i.e I_ph = I_L = 50A

The power in 3-phase star connection is given as

P = √3 × V_L × I_L × cos45°

= √3 × 440 × 50 × cos45°

P = 26940.3 watt

Power = 26.94 kW

The magnetic susceptibility expresses the responsiveness of a material to the applied magnetic field and can vary with the external applied magnetic field.

The symbol for magnetic susceptibility is χ and a magnetic susceptibility is a number with no units.

Materials with positive susceptibility have a field-induced within them that results in a total field that is greater than the strength of the magnetic field in which they are placed. Such materials are described as paramagnetic.

Materials with negative susceptibility have an induced field that opposes the field in which the material has been placed, so the talc field within the material is lower than the field in which they are placed. Such materials are described as diamagnetic.

For materials with positive susceptibility, the material is pushed toward stronger magnetic fields as it tends to lower potential energy whereas an opposite response for materials with negative susceptibility. Hence, materials with negative susceptibility (diamagnetic materials) are repelled and pushed toward weaker magnetic fields and materials with positive susceptibility (paramagnetic, ferromagnetic, ferromagnetic, and antiferromagnetic) are pulled toward stronger magnetic fields.

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

Reluctance = 30 ⁄ 15

Reluctance = 2 Amp-turns/Wb

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 = 120 turns

Current I = 0.1

F_m = 120 × 0.1

F_m = 12

Given

Line Voltage V_L = 400 V

Line current I_L = 50A

Phase angle φ = 53.13

The reactive power of three-phase AC circuit is given as

Q = √3 × V_L × I_L × sinφ

Q = √3 × 400 × 50 × sin 53.13°

Q = √3 × 400 × 50 × 0.8

Q = 27712.8 VAR

or

Q = 27.71 KVAR

Speed in the rotating disk

ξ = ½ ω.B.R²

ω = angular velocity = 2πN = 2 × 3.14 × 60 = 376.8 rad/sec

B = Magnetic Field = 3 T

Radius R = 10 cm = 0.1 m

Applying the above formula

ξ = ½ 376.8 × 3 × 0.1²

ξ = 5.65 V

The magnetic flux density at the center of an air core solenoid is given as

$B = \frac{{{\mu _o}NI}}{L}$

Where

B = Magnetic flux density = 5 × 10⁻³

N = Numbers of turns = 300 turn

I = Current = ?

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

µ_o = permeability of free space = 4π × 10^-7

$\begin{array}{l}5 \times {10^{ – 3}} = 4\pi \times {10^{ – 7}} \times \dfrac{{300 \times I}}{{0.5}}\\\\I = 6.63A\end{array}$

Eddy current losses in the transformer is given by

Eddy current losses = K_e × B_m² × f² × V ×t²

Where
K_e = Eddy current constant = 2
t = thickness of the core = 4 mm = 4 × 10⁻³
V = Volume of material = 20m³
B_m = Maximum flux density = ? 
f = frequency = 50 Hz
Eddy current losses = 6W

Now put the above data in the equation we get

6 = 2 × B²m × (50)² × (4 × 10^-3)² × 20

B²_m = 3.75

B_m = 1.94