Short Answer

Biot–Savart Law is a rule in physics that helps us calculate the magnetic field produced by a small current-carrying element. It states that the magnetic field at a point depends on the current, the length of the wire element, the distance from the point, and the angle between the wire and the line joining the point.

According to this law, the magnetic field becomes stronger when the current is large or the point is closer to the wire. It becomes weaker when the distance increases. This law is very important for understanding magnetic fields around wires, loops, and coils.

Detailed Explanation

Biot-Savart Law

Biot–Savart Law is a fundamental law of electromagnetism that describes the magnetic field produced by a small element of a current-carrying conductor. It was discovered by two French scientists, Jean-Baptiste Biot and Félix Savart. The law helps us understand how electric currents create magnetic fields and how the strength and direction of these fields can be calculated at any point in space.

This law applies to straight wires, circular loops, solenoids, and any shape of conductor. Using Biot–Savart Law, we can find the magnetic field produced at a point due to each small part of the conductor and add them up to get the total magnetic field.

Statement of Biot–Savart Law

Biot–Savart Law states:

The magnetic field (dB) produced at a point by a small current element (dl) is directly proportional to the current (I), the length of the element (dl), and the sine of the angle (θ) between the element and the line joining the point, and inversely proportional to the square of the distance (r²) from the element to the point.

Mathematically:

dB = (μ₀ / 4π) × (I dl sinθ / r²)

Where:

• dB = small magnetic field produced
• μ₀ = permeability of free space
• I = current
• dl = small length of conductor
• θ = angle between dl and r
• r = distance from conductor to the point

This law is used to calculate magnetic fields by integrating (or adding up) dB for all elements.

Understanding each term in Biot–Savart Law

1. Current (I)
   More current produces a stronger magnetic field.
2. Length element (dl)
   A small part of the wire contributes a small magnetic field.
3. Distance (r)
   The magnetic field becomes weaker as the distance increases.
   If the point is far away, the field is very small.
4. Angle (θ)
   The field is maximum when the angle is 90°
   (that is, sinθ = 1).
   It becomes zero when the element is pointing directly toward or away from the point.
5. Permeability (μ₀)
   This constant tells how much magnetic field is created in a vacuum.

Direction of the magnetic field using Biot–Savart Law

The direction of magnetic field (dB) is given by the right-hand thumb rule:

• Point the thumb in the direction of current
• Fingers curl in the direction of magnetic field

So, the magnetic field around a straight conductor forms circular loops.

Applications of Biot–Savart Law

Biot–Savart Law is used in many situations to calculate the magnetic field.

1. Magnetic field due to a straight wire

Using this law, we can calculate the field around a long straight current-carrying conductor.

2. Magnetic field at the center of a circular loop

Biot–Savart Law helps find the field produced by current flowing in a circular coil.

3. Magnetic field of a solenoid

A solenoid acts like many circular loops stacked together. This law helps calculate the field inside it.

4. Magnetic field in a toroid

Toroids use circular windings, and Biot–Savart Law helps calculate the magnetic field inside them.

5. Electromagnets

Designing electromagnets becomes easier using this law, as it helps predict magnetic strength.

6. Electrical machines

Motors, generators, and transformers use magnetic fields created by current loops.

Importance of Biot–Savart Law

Biot–Savart Law is important because:

• It gives the exact mathematical value of magnetic field
• It works for any shape of conductor
• It shows how magnetic field depends on current and distance
• It forms the foundation of Ampere’s Law
• It helps understand electromagnetic devices

It is similar to Coulomb’s Law in electrostatics but deals with magnetic fields instead of electric fields.

Comparison with Ampere’s Law (simple)

• Biot–Savart Law gives the magnetic field by adding contributions from all small wire elements.
• Ampere’s Law works for highly symmetrical cases like long straight wires and solenoids.

Biot–Savart Law is more general and works for all current shapes.

Physical meaning of Biot–Savart Law

The law tells us how a moving electric charge creates a magnetic field around it. Since electric current is made up of moving charges, a wire carrying current behaves like many moving charges producing magnetic fields.

This law explains:

• Magnetic field direction
• Magnetic field strength
• How current and distance affect the field

All magnetic fields in daily life—from motors to magnets—can be explained using this law.

Conclusion

Biot–Savart Law is a key law in electromagnetism that allows us to calculate the magnetic field produced by a small current element. It relates the magnetic field to current, distance, and angle. The law helps determine magnetic fields around straight wires, loops, solenoids, and many electrical devices. It forms the basis of understanding electromagnets, motors, transformers, and other magnetic systems. Knowing this law helps us understand how electricity and magnetism are connected.