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Biot Savart Law - Meaning, Formula, Example, Solution, Applications and Importance

 

Physicists acknowledge that electromagnetic force is a fundamental property of electromagnetism. Electromagnetic force and electric current are usually interconnected. The Biot-Savart Law describes the relationship between magnetic fields and electric current.

What is Biot-Savart Law?

According to Biot-Savart's law, a segment of the current-carrying cnductor produces a magnetic field. That segment is referred to as the element of current and is a vector quantity.

In the statement, the Biot-savarts law says that A point A's magnetic intensity (dB) is directly proportional to the current I flowing through a small element (dl).

What is the Formula of Biot-Savart’s Law?

Imagine a wire carrying current "i" facing a certain direction. Cut a small piece of the wire ds long. Consequently, its direction is parallel to the current, forming a vector. The value for this vector is ‘ids’.

One can apply Biot-Savart's Law to find the magnetic field produced at a point due to this small element. From the current element, let r represent the position vector of the point in question, and let θ represent the angle between them. The value by Biot-Savarts Law is given by:

dB= μ₀ i.ds x r/4ℼr²

Where

μ₀ represents the permeability of free space, which is equal to 4π × 10⁻⁷ TmA⁻⁷⁻¹.

The line of element and position vector should not have a zero angle, and the magnetic field is always perpendicular to them. The magnetic field's direction is shown by the thumb rule, in which the thumb shows the conventional current's direction, while the curl is along the magnetic field.

Example:

A wire contains a current of 5A. What would be the magnetic field at a point situated 4m away from the wire and the angle between the segment of current and the point is 30°

Solution:

Current in the conductor (i): 5A

Radial Length (r): 4m

The angle between the current segment and point (θ)= 30°

Formula for Biot-Savarts Law

dB= dB= μ₀ i.ds rsin θ/4ℼr²

Substituting the values for each variable

dB= (4ℼx 10⁻⁷ TmA⁻¹x 5A 4m x sin 30°)/ 4ℼ x 4mx 4m

dB= 2.5x10⁻⁷/16T

dB = 6.25x10⁻⁸T

Biot-Savart's Law: Applications

Below are a few examples of Biot-Savart's Law applications.

  • It is used to calculate the magnetic field in various positions with respect to the current-carrying conductor.
  • Even atomic and molecular magnetic responses can be calculated with the Biot–Savart law.
  • The formula is also used to calculate the velocity caused by vortex lines in aerodynamic theory.

Biot-Savart Law's importance

The following are some of the reasons why the Biot-Savart law is important:

  • Coulomb's law in electrostatics is equivalent to Biot-Savart's law.
  • Even very small conductors that carry current are subject to the law.
  • If the current distribution is symmetrical, the law applies.
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