Question

Among the following, Ampere’s circuital law is represented by:

• A. \( \oint B \cdot dl = 0 \)
• B. \( \oint B \cdot dl = \mu_0 I \)
• C. \( \oint B \cdot dl = \frac{\mu_0}{I} \)
• D. \( \oint B \cdot dl = \mu_0 \)

Hint:

Ampere's circuital law relates the magnetic field around a closed loop to the current passing through the loop. It is widely used to calculate the magnetic field produced by various current configurations.

Answer 1

The Correct Option is B

Recall Ampere’s Circuital Law:
Ampere’s circuital law states that the line integral of the magnetic field \( B \) along a closed loop is proportional to the current enclosed by that loop. The mathematical expression is: \[ \oint B \cdot dl = \mu_0 I \] where:
\( B \) is the magnetic field,
\( dl \) is the differential length element along the loop,
\( \mu_0 \) is the permeability of free space, and
\( I \) is the current enclosed by the loop.
Step 2: Identify the correct representation of Ampere's law: The correct representation of Ampere’s circuital law is: \[ \boxed{\oint B \cdot dl = \mu_0 I} \]