Tasks #01
i. Explain Ampere’s law
Ampere’s law states that “The magnetic field around a closed loop is proportional to the
electric current passing through the loop”
𝐵 =
𝜇₀𝐼
2𝜋𝑟
ii. Describe Faradays law
Faradays law states that “The electromotive force (emf) induced in a closed circuit is
proportional to the rate of change of magnetic flux through the circuit”
𝑑∅
e = -N 𝑑𝑡
iii. Describe Biot-Savart law
The magnetic field intensity d𝑯 produced at a point P due to a differential current
element IdL is,
1. Proportional to the product of the current I and differential length dL.
2. The sine of the angle between the element and the line joining point P to the
element.
3. And inversely proportional to the square of the distance R between point P and the
element.
the Biot-Savart law can be stated as,
d𝑯 α
d𝑯 =
Where
In SI units,
𝐼𝑑𝐿𝑠𝑖𝑛𝛳
𝑅2
𝑘𝐼𝑑𝐿𝑠𝑖𝑛𝛳
𝑅2
k = Constant of proportionality
1
k = 4𝜋 hence
Hence, d𝑯 =
𝐼𝑑𝐿𝑠𝑖𝑛𝛳
4𝜋𝑅 2
Task#02
i. Explain magnetic circuits
Magnetic circuits this are the circuit which are made up of one or more closed loop path
containing
(a) A magnetic field is the state of the space in the vicinity of a permanent magnet or an
electric current throughout which the magnetic forces produced by the magnet or current
are discernible.
(b) Magnetic flux ᶲ is the amount of magnetic field produced by a magnetic source. The unit
of magnetic flux is the weber, Wb. If the flux linking one turn in a circuit changes by one
weber in one second, a voltage of one volt will be induced in that turn.
(c) Magnetic flux density B is the amount of flux passing through a defined area that is
perpendicular to the direction of the flux.
ii. Explain displacement current
Is the current that is produced by the rate of change of the electric displacement field, is the quantity
explained in Maxwell’s equation and its measured in Ampere (A). Displacement current are
produced by a time varying electric field rather than moving charges
iii. Describe transformer and motional EMF
Transformer is the device that transfers electric energy from one alternating current (AC) circuit
to one or more circuits, either increasing (stepping up) or reducing (stepping down) the voltage
e.g. To reduce the voltage of conventional power circuits to operate low-voltage devices
Motional EMF is the emf induced in a conducting rod when it moves in a region of magnetic
field. Motional emf is calculated by E=vBl. Where B is the magnetic field and l is the length of
the rod and v is the velocity of rod perpendicular to the length of the rod.
iv. Derive Maxwell equation (differential and integral form)
The basic Maxwell's equations for static fields are derived from Faraday's law, Ampere circuit law,
Gauss’s law for electrostatic field and Gauss's law for magneto static field.
A) Maxwell's Equation Derived from Faraday's Law
∮ 𝑬 • 𝑑𝐿 = 0
∮ 𝑬 • 𝑑𝐿 = ∫ (∇ × 𝑬) • 𝑑𝑺 = 0
𝑠