Magnetic Field inside a long straight Solenoid | in HINDI | EduPoint

In this video in Hindi we talked about the basics of a solenoid and evaluated the magnetic field inside and outside of a long straight solenoid. Solenoid is a current carrying coil. And as we know that current creates magnetic field around it, the solenoid also creates magnetic field. We found that the magnetic field inside a solenoid of n number of turns pr unit length and carrying current I is μ_0nI. Surprisingly, the magnetic field does not depend upon its length or cross sectional area. So if two coils have same density of turns and carrying same amount of current, it does not matter which coil is longer or wider; both of them will create same magnetic field inside. To evaluate the magnetic field inside we used Ampere's circuital law.
Ampere’s circuital law states that the closed line integral of magnetic field around a current carrying conductor is equal to absolute permeability times the total current threading the conductor.
Mathematically,
∮ B ⃗ . dl ⃗ = μ_0 I
Other related and important topics :
Biot - Savart's law :-
Biot and Savart found that the magnetic field at point P due to the elementary portion of the wire is,
Directly proportional to the current, i.e.,
dB ∝ I .
Directly proportional to the length of the wire, i.e.,
dB ∝ dl.
Directly proportional to the sine of angle between the direction of flow of current and line joining the elementary portion and the point P, i.e.,
dB ∝ sinθ.
Inversely proportional to thesquare of the distance of the point P from the elementary portion, i.e.,
dB ∝ 1/(r^2)
Considering all the factors, we have
dB ∝ (I dl sinθ)/(r^2)
or, dB = k (I dl sinθ)/r^2
where, k is constant of proportionality.
In vacuum,
k = μ_0/4π = 〖10〗^(-7) T A^(-1) m
where, μ_0 is called absolute permeability of free space.
Therefore, in S.I., Biot-Savart’s law can be expressed as
dB = μ_0/4π (I dl sinθ)/(r^2)
Direction of dB ⃗ :- the direction of this magnetic field is same as the direction of the vector dl ⃗ × r ⃗. It follows that the direction is perpendicular to the plane of the paper and directed inwards.
Hence in vector notation,
dB ⃗ = μ_0/4π (I dl ⃗ × r ̂ )/r^2 = μ_0/4π (I dl ⃗ × r ⃗ )/r^3
Click the link to watch the video on Biot-Savart's law :
• Biot Savart's Law and ...
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Arijit Daripa
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