Question

State and explain Ampere’s circuital law.

Hint:

Ampere's circuital law is a fundamental law of electromagnetism that helps in calculating the magnetic field produced by current-carrying conductors using symmetry and geometry.

Answer 1

Step 1: Ampere's circuital law states that the line integral of the magnetic field \( \vec{B} \) around a closed loop is proportional to the total current \( I_{\text{enc}} \) enclosed by the loop. Mathematically, it is expressed as:
\[ \oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}} \] where:
\( \oint \vec{B} \cdot d\vec{l} \) is the line integral of the magnetic field around a closed loop,
\( \mu_0 \) is the permeability of free space (\( \mu_0 = 4\pi \times 10^{-7} \, \text{}^2 \)),
\( I_{\text{enc}} \) is the total current enclosed by the loop.
Step 2: The law implies that the magnetic field around a current-carrying conductor is directly proportional to the current flowing through the conductor. It is commonly used to determine the magnetic field around simple geometries like straight wires, solenoids, and loops.