The derivation of Biot Savart Law is provided in this article. Biot-Savart law, named after Jean-Baptiste Biot and Felix Savart, is defined as an equation that explains the magnetic field generated by constant electric current. It plays a similar role to that of Coulomb’s law in electrostatics but in magnetostatics. Biot-Savart law relates the magnetic field to the magnitude, length, direction, and proximity of electric current. This law is mainly used in electromagnetism.
| Table of Contents |
Biot Savart Law Derivation
Following is the derivation of the Biot-Savart law.
Using electric fields that are generated by stationary charges, we get
Where Φ: electric scalar potential
The expression obtained from electric fields that are generated by stationary charges
Below is the Biot-Savart law expression before the substitution of j
Substituting for j (current density) where I is the vector current and dl is element length
After substituting for j, we obtain the Biot-Savart expression
Biot-Savart Law for Point Charges
Following is the Biot Savart-law derivation for point charge:
Maxwell’s equation is used for expressing electric field and magnetic field
Where,
q: charged particle
v: constant velocity.
Above is the equation for the Biot-Savart law for point charge which is derived in 1888 by Oliver Heaviside.
This was the derivation of the Biot-Savart law. Stay tuned with BYJU’S and learn various other Physics related topics.
Related Physics Articles:
| What is Velocity? | Average Velocity |
| The SI Units | Force Push And Pull Action |
Solved Problems on Biot-Savart Law
Q1. Determine the magnitude of the magnetic field of a wire loop at the centre of the circle with radius R and current I.
Ans: The magnitude of the magnetic field of the wire loop is given as:
Q2. A circular coil of radius 5 × 10-2 m and with 40 turns is carrying a current of 0.25 A. Determine the magnetic field of the circular coil at the centre.
Ans: The radius of the circular coil = 5 × 10-2 m
Number of turns of the circular coil = 40
Currently carried by the circular coil = 0.25 A
The magnetic field is given as:
Q3. Determine the magnetic field at the centre of the semicircular piece of wire with a radius 0.20 m. The current carried by the semicircular piece of wire is 150 A.
Ans: The radius of the semicircular piece of wire = 0.20 m
Current carried by the semicircular piece of wire = 150 A
Magnetic field is given as:
The differential form of Biot-Savart law is given as:
This is the derivation of Biot Savart law. Stay tuned with BYJU’S and learn various other Physics related topics.
Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!
Select the correct answer and click on the “Finish” button
Check your score and answers at the end of the quiz
Visit BYJU’S for all Physics related queries and study materials
Your result is as below
Comments