Biot-Savart Law

We know that electromagnetism is an important branch of Physics that deals with electromagnetic force. It typically deals with magnetic force and electric current. Let us know about the law that relates magnetic fields to the electric current – Biot-Savart Law.

What is Biot-Savart Law?

Biot-Savart’s law is an equation that gives the magnetic field produced due to a current carrying segment. This segment is taken as a vector quantity known as the current element.

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

Consider a current carrying wire ‘i’ in a specific direction as shown in the above figure. Take a small element of the wire of length ds. The direction of this element is along that of the current so that it forms a vector ids.

To know the magnetic field produced at a point due to this small element, one can apply Biot-Savart’s Law. Let the position vector of the point in question drawn from the current element be r and the angle between the two be θ. Then,

Where, μ₀ is the permeability of free space and is equal to 4π × 10^-7 TmA^-1.

The direction of the magnetic field is always in a plane perpendicular to the line of element and position vector. It is given by the right-hand thumb rule where the thumb points to the direction of conventional current and the other fingers show the magnetic field’s direction.

In the figure shown above, the direction of the magnetic field is pointing into the page.

Applications of Biot-Savart’s Law

Some of Biot-Savart’s Law applications are given below.

• We can use Biot–Savart law to calculate magnetic responses even at the atomic or molecular level.
• It is also used in aerodynamic theory to calculate the velocity induced by vortex lines.

Importance of Biot-Savart Law

Following are the importance of the Biot-Savart law:

• Biot-Savart law is similar to Coulomb’s law in electrostatics.
• The law is applicable for very small conductors too which carry current.
• The law is applicable for symmetrical current distribution.