According to Ampere's Law, what is the line integral of the magnetic field around a closed loop equal to?

1 question

1 item

Q: According to Ampere's Law, what is the line integral of the magnetic field around a closed loop equal to?

Solution: Ampere's Law states that the line integral of B around a closed loop is μ₀ times the total current through the loop.

Steps: 6

Step 1: Understand that Ampere's Law relates the magnetic field (B) to electric current.
Step 2: Recognize that a closed loop is an imaginary path that forms a complete circle.
Step 3: Know that the line integral of B means you are adding up the magnetic field along that closed loop.
Step 4: Identify that μ₀ is a constant called the permeability of free space, which helps relate current to magnetic fields.
Step 5: Realize that the total current through the loop is the sum of all currents that pass through the area enclosed by the loop.
Step 6: Combine these ideas to conclude that the line integral of B around the closed loop equals μ₀ times the total current through the loop.