# Biot Savart Law | What Is the Biot-Savart Law?

Biot Savart law, in physics, a fundamental quantitative relationship between an electric current and the magnetic field it produces, based on the experiments in 1820 of the French scientists Jean-Baptiste Biot and Félix Savart.

An electric current flowing in a conductor, or a moving electric charge, produces a magnetic field, or a region in the space around the conductor in which magnetic forces may be detected. The value of the magnetic field at a point in the surrounding space may be considered the sum of all the contributions from each small element, or segment, of a current-carrying conductor. The Biot-Savart law states how the value of the magnetic field at a specific point in space from one short segment of current-carrying conductor depends on each factor that influences the field. In the first place, the value of the magnetic field at a point is directly proportional to both the value of the current in the conductor and the length of the current-carrying segment under consideration.

The value of the field depends also on the orientation of the particular point with respect to the segment of current. If the line from the point to the short segment of current makes an angle of 90° with the current segment or lies straight out from it, the field is greatest. As this angle gets smaller, the field of the current segment diminishes, becoming zero when the point lies on a line of which the current element itself is a segment. In addition, the magnetic field at a point depends upon how far the point is from the current element. At twice the distance, the magnetic field is four times smaller, or the value of the magnetic field is inversely proportional to the square of the distance from the current element that produces it.

## Biot Savart Law Equation

Using the Biot-Savart Law requires calculus. That’s why there’s a dB and dl. Those are infinitesimal magnetic field elements and wire elements. So we’d have to integrate with respect to those elements. But we can use a simpler version of the law for a perfectly straight wire.

If we straighten out the wire and do some calculus, the law comes out as muu-zero I divided by 2pir. Or in other words, the magnetic field, B, measured in teslas is equal to the permeability of free space, muu-zero, which is always 1.26 x 10^-6, multiplied by the current going through the wire, I, measured in amps, divided by 2pi times the radius away from the wire, r, measured in meters. So this equation helps us figure out the magnetic field at a radius r from a straight wire carrying a current I.

The equation gives us the magnitude of the magnetic field, but a magnetic field is a vector, so what about the direction? The magnetic field created by a current-carrying wire takes the form of concentric circles. But we have to be able to figure out if those circles point clockwise or counter-clockwise (say, from above). To do that we use a right-hand rule.

I want you to give the screen a thumbs up, right now. I’m serious – give the screen a thumbs up with your right hand. It has to be with your right hand. If you point your thumb in the direction of the current for this wire, your fingers will curl in the direction of the magnetic field. They’ll follow the arrows of the concentric circles. And that’s how you figure out the direction.

## Mathematical Representation

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

Consider a wire carrying a current I in a specific direction as shown in the figure. Take a small element of the wire of length dl. The direction of this element is along that of the current so that it forms a vector Idl. If we want to know the magnetic field produced at a point due to this small element, then we can use the Biot-Savart’s Law.

The magnitude of the magnetic field dB at a distance r from a current carrying element dl is found to be proportional to I and to the length dl. And is inversely proportional to the square of the distance |r|. The direction of the Magnetic Field is perpendicular to the line element dl as well as radius r.

Thus the vector notation is given as, dB α Idl × r / r^{3 }= (μ_{0 /} 4π ) × (Idl × r / r^{3}),where μ_{0}/4π is a constant of proportionality. The above expression holds when the medium is a vacuum. Therefore the magnitude of this field is:

|dB| = (μ_{0} / 4π) × (Idl sinθ / r^{2})

## Biot Savart Law Applications

The applications of Biot Savart Law include the following

- This law can be used for calculating magnetic reactions even on the level of molecular or atomic.
- It can be used in the theory of aerodynamic for determining the velocity encouraged with vortex lines.

Thus, this is all about biot savart law. From the above information finally, we can conclude that the **magnetic field** because of a current element can be calculated by using this law. And, the magnetic field because of some configurations such as a circular coil, a disk, a line segment, was determined by using this law.

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