Biot-Savart law

 

MODULE 3: MAGNETOSTATICS

BIO-SAVART LAW, DIVERGENCE AND CURL OF STATIC MAGNETIC FIELD; VECTOR POTENTIAL AND CALCULATING IT FOR A GIVEN MAGNETIC FIELD USING STOKES’ THEOREM; THE EQUATION FOR THE VECTOR POTENTIAL AND ITS SOLUTION FOR GIVEN CURRENT DENSITIES.

Biot-Savart law

The Biot-Savart law describes the magnetic field produced by a steady current flowing in a conductor. The law mathematically expresses the magnetic field contribution (dB) at a point in space due to an infinitesimally small current element (Idl).

Biot-Savart law named after the French physicists Jean-Baptiste Biot and Félix Savart 

steady current  =  constant current

current element = the product of current and infinitesimal conductor length

Statement

Biot-savart law states that the magnetic field due to a current carrying conductor at a distance r is inversely proportional to the square of the distance r, and the magnetic field is directly proportional to the product of current element (Idl) and sine of angle q between current element and distance r.

 

 According to Biot-Savart law

 

combining these three relations,we get

 

This is the basic formula of Biot-Savart law.

here

 

Question 01

For a straight current-carrying wire, how does the magnitude of the magnetic field vary with the distance from the wire according to the Biot-Savart law?

A. Linearly increases with distance
B. Quadratically increases with distance
C. Inversely proportional to the square of the distance
D. Inversely proportional to the distance

Answer: D. Inversely proportional to the distance

Question 02

What does the Biot-Savart law describe in electromagnetism?

A. Electric field generated by a stationary charge
B. Magnetic field produced by a steady current
C. Relationship between voltage and current in a circuit
D. Electrostatic forces between charged particles

Answer: B. Magnetic field produced by a steady current

Question 03

In the Biot-Savart law, what does Idl represent?

A. Electric current in the conductor
B. Infinitesimal current element
C. Permeability of free space
D. Distance between two current-carrying wires

Answer: B. Infinitesimal current element

Question 04

What physical quantity does the permeability of free space μ₀​ represent in the Biot-Savart law?

A. Electric charge
B. Electric field
C. Magnetic permeability
D. Permittivity

Answer: C. Magnetic permeability

Question 05

In the Biot-Savart law, what happens to the magnetic field as the distance from the current element increases?

A. It remains constant.
B. It decreases inversely with distance.
C. It increases linearly with distance.
D. It varies depending on the direction of the current.

Answer: B. It decreases inversely with distance.

Question 06

Which of the following equations represents the Biot-Savart law in integral form?

 

Answer: B 

 

 

Question 07

What does the Biot-Savart law primarily deal with in terms of current characteristics?

A. Time-varying currents
B. Non-steady currents
C. Steady currents
D. Alternating currents

Answer: C. Steady currents

Question 08

For a straight current-carrying wire, how does the magnitude of the magnetic field vary with the distance from the wire according to the Biot-Savart law?

A. Linearly increases with distance
B. Quadratically increases with distance
C. Inversely proportional to the square of the distance
D. Inversely proportional to the distance

Answer: D. Inversely proportional to the distance