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Magnetism is a phenomenon resulting from the movement of electric charges and associated with magnetic fields. This movement can take many different forms. It could be the motion of an electron in an atomic orbital or an electric current in a conductor, or charged particles travelling through space. Magnetism is also linked to elementary particles that have a spin feature, such as the electron.
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Key Terms: Magnetism, Magnetic field, Biot Savart Law, Ampere Law, Electric current, Magnetic induction, Vector, Electron, Phenomenon, Atomic orbital
Magnetic Field
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Magnetic field is the area around a moving charge where its magnetic effects can be seen on the moving charge (electric current). Magnetic field intensity, commonly known as magnetic induction vector, is a vector quantity. The magnetic field can be calculated in two ways. The magnetic field owing to an infinitesimally small current carrying wire at a point is given by the biot-Savart law, while the magnetic field of a systematic configuration carrying a steady current is calculated by ampere's law.
Magnetic field lines
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Biot Savart Law
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In the Biot-Savart Law, an electric current generates a magnetic field by means of a continuous current. Magnetism determines the intensities, directions, lengths, and proximity of electric currents. Biot-Savart's law is consistent with Ampere's circuit theory and Gauss' theorem. Magnetic fields obey the Biot-Savart law in much the same way that electrostatic fields do.
Biot-Savart Law Video Lecture
Application of Biot Savart Law
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In electromagnetism, Biot-law Savart's has a variety of applications. The following are two of them:
(a) Magnetic induction at a place caused by a long straight current-carrying wire.
(b) The induction of magnetic fields at the centre of a current-carrying circular coil.
- Magnetic induction, or the magnetic field created by a long straight wire carrying current, at a given point:
Assume PQ is a long, straight wire with a current of I amperes flowing across it. It is necessary to determine magnetic induction or magnetic field at point X at a distance r from the wire.
Magnetic induction, or the magnetic field created by a long straight wire carrying current
Let's take a very short portion AB of that wire. Its length should be dl. Assume that the distance between the portion's centre point O and the point X is r, and that the angle XOQ = θ
So, given current element point X, the magnitude of the magnetic field derived by solving the Biot-Savart Law is,
B=\(\frac{μoI}{2a}\)
The magmatic intensity produced for a current-carrying wire or magmatic poles is dependent on which quantity.
The intensity of the magnetic field created by a current-carrying wire is independent of the surrounding medium. The intensity of the magnetic field created by magnetic poles, on the other hand, is dependent on the surrounding material. The magnetic field generated along the wire's length is zero.
- Magnetic induction at the centre of the current carrying circular coil
Assume that the flow of I ampere current through a conductor produces a magnetic field around an infinitely small piece dl metre of the conductor. Let the distance between a location and the mid-point of this section of the wire be r metres. If this distance produces an "angle" with the direction of current flow, then the magnetic induction or magnetic field at that location is, according to Biot Savart's law.
dB=(μo/4)(idl/r2) sin θ
Magnetic induction at the centre of the current carrying circular coil
Right Hand Thumb Rule
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Right thumb pointing in the direction of the velocity (v), index finger pointing in the direction of magnetic field (B), and middle finger-pointing in the direction of the resulting magnetic force (F) will be your guide in determining the direction of the magnetic force on a positive moving charge. Charges that are negative will be affected by a force in the opposite direction.
Right Hand Thumb Rule
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Ampere’s Law
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The line integral of a magnetic field around a closed path is equal to the product of the magnetic permeability of that space and the total current across the area circumscribed by that path, according to Ampere's law.
Ampere’s Law Formula is given by,
Formula of Magnetism
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Magnetic Field due to straight current carry wire.
Where,
B = Strength of the magnetic field
d = Distance
I = Current in wire
μo= Permittivity of free space
Curie Law in Magnetism
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A paramagnetic substance's magnetic susceptibility is inversely related to its absolute temperature.
M = C \(\frac{B}{T}\)
Where
M = Magnetic susceptibility of a paramagnetic substance
C = Curie’s Constant
B = Magnetic Field
T = Absolute temperature
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Things to Remember
- A wire carrying an electric current generates a magnetic field with closed field lines all around it.
- Point the thumb in the direction of the current, and the fingers curl in the direction of the magnetic field loops formed by it, to calculate the magnetic field direction from a current.
- A current segment can be used to determine the magnetic field strength using the Biot-Savart Law. It is reduced to the form for the basic situation of an infinite straight current-carrying wire.
- Ampere's Law, which links magnetic field and current in a generic way, is a more fundamental law than the Biot-Savart law.
Sample Questions
Ques. What is the magnetic field of a circular coil’s centre? (1 mark)
Ans. The magnetic field in the centre of a circular coil is calculated using the permeability of an empty space, the coil’s radius, and the current flowing through it.
Ques. On the axis of a circular current loop, what is the magnetic field? (1 mark)
Ans. The magnetic field is strongest in the centre and gradually diminishes as we go away from the circular loop's centre along the loop's axis.
Ques. What does a current-carrying loop's magnetic field look like? (3 marks)
Ans. Bx = μ0IRx22(x2 +R2)3/2i is the magnetic field on the axis of a current-carrying loop, where x is the distance of that point on the axis from the loop's centre, R is the loop's radius, and I is the current flowing in the loop. Put (x=0) in the above calculation for the magnetic field at the loop's centre.and I is the current flowing in the loop. Put (x=0) in the above calculation for the magnetic field at the loop's centre.
Ques. Define circular loop? (2 marks)
Ans. A circular loop is made up of a lot of extremely small straight wires arranged in a circle. A magnetic field is created when an electric current flows through a circular coil of wire. At the centre of the circular wire, the field lines become straight and perpendicular to the coil plane.
Ques. Name one feature that the Biot Savart law cannot compute? (2 marks)
Ans. Electric field intensity cannot be calculated using the Biot Savart law. It is used for calculating the magnetic field intensity. Which is further used for calculating the flux density and permeability using the formula B= μoNI/2R.
Ques. Define Biot Savart Law? (2 marks)
Ans. The magnetic field due to a current carrying conductor at a distance point is inversely proportional to the square of the distance between the conductor and the point, and the magnetic field is directly proportional to the length of the conductor, current flowing in the conductor, according to the Biot Savart law.
Ques. What are the applications of Biot Savart Law? (3 marks)
Ans.
- Magnetic fields in space caused by any current carrying conductor are calculated using the Biot-Savart equation.
- The force between two long and parallel current carrying conductors is calculated using the Biot-Savart law.
- The magnetic field on the axis of a circular current loop is calculated using the Biot-Savart equation.
Ques. What are the two properties of a material used to make permanent magnets? (2 marks)
Ans.
- It has a high retentivity, resulting in a strong magnetic field.
- High coercivity ensures that high magnetic fields, temperature changes, and slight mechanical damage do not degrade its magnetism.
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