In a circular path of radius r around a long straight wire carrying current I, w

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Question: In a circular path of radius r around a long straight wire carrying current I, what is the line integral of the magnetic field?

Options:

Correct Answer: μ₀I

Solution:

The line integral of B around the path is equal to μ₀I by Ampere\'s Law.

In a circular path of radius r around a long straight wire carrying current I, what is the line integral of the magnetic field?

In a circular path of radius r around a long straight wire carrying current I, what is the line integral of the magnetic field?

Step 1: Understand that we have a long straight wire carrying a current I.
Step 2: Recognize that the magnetic field (B) created by this current forms circular loops around the wire.
Step 3: Identify the radius of the circular path around the wire, which is given as r.
Step 4: Recall Ampere's Law, which states that the line integral of the magnetic field B around a closed loop is equal to μ₀ times the total current I passing through the loop.
Step 5: Apply Ampere's Law to our circular path: the line integral of B around the path is equal to μ₀I.
Step 6: Conclude that the line integral of the magnetic field B around the circular path of radius r is μ₀I.

Ampere's Law – Ampere's Law relates the magnetic field around a closed loop to the electric current passing through the loop.
Magnetic Field due to a Long Straight Wire – The magnetic field generated by a long straight wire carrying current is circular and can be calculated using Ampere's Law.
Line Integral of Magnetic Field – The line integral of the magnetic field around a closed path is used to determine the total magnetic effect due to the current enclosed by the path.