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 posits that the line integral of the magnetic field \( \vec{B} \) along a closed path is directly proportional to the net current \( I_{\text{enc}} \) threading that path. The mathematical formulation is:
\[\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}\]In this equation:
\( \oint \vec{B} \cdot d\vec{l} \) represents the line integral of the magnetic field over a closed loop,
\( \mu_0 \) is the magnetic constant (permeability of free space, with a value of \( 4\pi \times 10^{-7} \, \text{}^2 \)),
\( I_{\text{enc}} \) denotes the total current that passes through the area bounded by the loop.
Step 2: This law indicates that the magnetic field generated by a current-carrying wire is directly proportional to the magnitude of the current. It is a fundamental tool for calculating the magnetic field produced by symmetric current distributions, such as those found in straight conductors, solenoids, and current loops.