Biot-Savart Law-

 

Biot-Savart law is meant for calculating the magnetic field produced by the current element of a thin wire.

 

What is a Current Element? Current element is a small length segment of the wire which carries the same current flowing in the wire and whose direction is same as direction of current. It is a vector quantity. Mathematically, it is given by the product of current flowing in the wire and a small length of the wire. So,     Its SI unit is ampere meter (Am).

 

Consider a current element Idℓ of a thin wire AB carrying current I. Let-

• P be a point where the magnetic field dB due to the current element Idℓ is to be calculated.
• r be the position vector of point P relative to the current element Idℓ.
• θ be the angle between Idℓ and r.

 

This is shown below-

 

 

According to Biot-Savart law, the magnitude of the magnetic field dB due to the current element is-

• directly proportional to the current I flowing through the wire

dB ∝ I

• directly proportional to the length dℓ of the current element

dB ∝ dℓ

• directly proportional to the sine of the angle between Idℓ and r

dB ∝ sinθ

• inversely proportional to the square of the distance r of point P from the current element

dB ∝ 1/r²

 

Combining all these factors, we get-

 

 

where K is a constant of proportionality which depends upon the following factors-

1. the nature of medium between the observation point P and the current element Idℓ
2. the system of units chosen

 

For free space and in SI units, we have-

 

 

Here, μ₀ is a constant called as permeability of free space.

 

So, Biot-Savart law may be expressed as-

 

(For free space)

 

This formula helps to calculate the magnitude of magnetic field at any point due to the current element of a thin wire.

 

Biot-Savart Law in Vector Form-

 

From the scalar form of Biot-Savart law, we have-

 

 

Multiplying numerator and denominator by r, we get-

 

 

Thus, Bio-Savart law in vector form can be stated as-

 

 

From here, the direction of magnetic field due to the current element is the direction obtained by taking the cross product Idℓ x r.

 

Defining One Tesla From Biot-Savart Law-

 

From Biot-Savart law, the magnitude of magnetic field due to the current element at any point is given by-

 

 

If, we have-

• Current flowing in the wire (I) = 1 A
• Length of the current element (dℓ) = 1 m
• Distance of observation point from the current element (r) = 1 m
• Angle between Idℓ and r (θ) = 90°

 

Then, dB is given by-

 

 

Thus, one tesla may be defined as-

 

One tesla is 107 times the magnetic field produced by a thin conducting wire of length one meter and carrying current of one ampere at a distance of one meter from it and perpendicular to it.

 

MCQs Quiz-

MCQs Quiz on Biot-Savart Law

 

Worksheet-

Worksheet on Biot-Savart Law

 

Next Article-

Magnetic Field At Center of Circular Current Loop

 

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