What is the Difference Between Coulomb’s Law and Biot Savart Law

Both Coulomb’s law and Biot Savart law describe the relationship between a source and a resulting field. However, there are distinct differences between Coulomb’s law and Biot Savart law.

What is the difference between Coulomb’s law and Biot Savart law? Coulomb’s law applies to electric charges while Biot Savart law applies to electric currents.

Key Areas Covered

1. What is Coulomb’s Law 
      – Definition, Features
2. What is Biot Savart Law
      – Definition, Features
3. Similarities Between Coulomb’s Law and Biot Savart Law
      – Outline of Common Features
4. Difference Between Coulomb’s Law and Biot Savart Law
      – Comparison of Key Differences
5. FAQ: Coulomb’s Law and Biot Savart Law
      – Answers to Frequently Asked Questions

Key Terms

Coulomb’s Law, Biot Savart Law

What is Coulomb’s Law

Coulomb’s law states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. The equation to find the relevant force is as follows.

F = k * (q1 * q2) / r2.

F is the electrostatic force between the two charges

k is Coulomb’s constant, a proportionality constant with a value of approximately 8.988 × 109N⋅m2/C2

q1 and q2 are the magnitudes of the charges while r is the distance between the charges.

The direction of the electrostatic force is along the line connecting the two charges. If the charges are the same (positive and positive or negative and negative), the force is repulsive, but if the charges are opposite (positive and negative), the force is attractive.

There are many applications of Coulomb’s law. In electronics and electrical engineering, it is used to design electrical components, printed circuit board design, and electrostatic discharge protection. Moreover, in material science, it is used in the development of new materials, dielectric materials, and semiconductors. Additionally, in medical physics, it is used in radiation therapy and medical imaging.

What is Biot Savart Law

Biot Savart law is found in the field of electromagnetism. The law states that the magnetic field at a point due to a current element is directly proportional to the magnitude of the current element, the sine of the angle between the current element and the line joining the point to the current element, and inversely proportional to the square of the distance between the point and the current element.

The relevant equation is given below.

dB = (μ_°/4π) * (Idl × r̂) / r²

where:
dB is the magnetic field at the point due to the current element.
μ_° is the permeability of free space, a constant that relates magnetic fields to electric currents.
Idl is the current element, a small segment of the wire carrying current.
r̂ is a unit vector pointing from the current element to the point where the magnetic field is being calculated.
r is the distance between the current element and the point.

Biot Savart law is used in many applications. It is used in calculating magnetic fields, derivation of Ampere’s law, evaluating the magnetic responses of atoms and molecules at the molecular level, and calculating the velocity induced by vortex lines in aerodynamic theory and electrical devices.

Similarities Between Biot Savart Law and Coulomb’s Law

1. Both Coulomb’s law and Biot Savart law follow an inverse square law.
2. Furthermore, both laws are linear.

Difference Between Biot Savart Law and Coulomb’s Law

Definition

• Coulomb’s law deals with electric fields generated by stationary electric charges, whereas Biot Savart law deals with magnetic fields generated by moving electric charges.

Type of Field

Coulomb’s law describes the electric field due to a point charge. However, Biot-Savart law describes the magnetic field due to a current element.

Nature of the Fields

• In Coulomb’s Law, the electric field lines are radial, pointing directly away from or towards the point charge. However, in Biot-Savart law, the magnetic field lines are circular, encircling the current-carrying wire. Moreover, the direction of the field is determined by the right-hand rule.

Conclusion

Although both Coulomb’s law and Biot Savart law deal with inverse square relationships and have applications in electromagnetism, they describe different phenomena and have distinct mathematical formulations. Basically, Coulomb’s law applies to electric charges while Biot Savart law applies to electric currents.

FAQ: Coulomb’s Law and Biot Savart Law

1. What is the difference between Biot-Savart law and Ampere’s law?

Biot-Savart law gives the magnetic field at a point due to a current element, while Ampere’s law relates the line integral of the magnetic field around a closed loop to the total current passing through the loop.

2. What are the limitations of Biot-Savart law?

The Biot-Savart law is limited to steady currents and cannot be used to calculate magnetic fields from time-varying currents. It also requires knowledge of the exact path of the current.

3. What are the applications of Biot-Savart law?

The Biot-Savart law determines the magnetic field produced by a current-carrying wire. Moreover, it has applications in various fields, including electromagnetism, electrical engineering, and physics.

4. What are the assumptions of Biot-Savart law?

The Biot-Savart law assumes that the current is steady and that the magnetic field is produced by a moving charge in a vacuum.

5. What does Coulomb’s law depend on?

Coulomb’s law depends on the magnitude of the charges and the distance between them.

Reference: 

1. “Biot-Savart Law.” Encyclopedia Britannica. 
2. “Coulomb’s Law.” Encyclopedia Britannica. 

Image Courtesy: 

1. “Magnetic field element (Biot-Savart Law) r1r2” by Guy vandegrift (CC BY-SA 4.0) via Commons Wikimedia

2. “CoulombsLaw scal” by User:Dna-Dennis (CC BY 3.0) via Commons Wikimedia