A wire oriented along the z-axis carries a current of 19.0 A. It is found that the line integral of the magnetic field along a square loop of side length b oriented in the x-y plane and centered at the wire is 10 T m. What is the line integral if the length of the square loop is changed to 3 b. 20 T m. 30 T m. 10 T m. 2.5 T m.
Question
A wire oriented along the z-axis carries a current of 19.0 A. It is found that the line integral of the magnetic field along a square loop of side length b oriented in the x-y plane and centered at the wire is 10 T m. What is the line integral if the length of the square loop is changed to 3 b. 20 T m. 30 T m. 10 T m. 2.5 T m.
Solution
The line integral of the magnetic field around a loop is given by Ampere's Law, which states that it is equal to the current enclosed by the loop times the permeability of free space (μ0). In this case, the current is constant and the permeability of free space is a constant, so the line integral is proportional to the length of the loop.
In the original scenario, the line integral around a square loop of side length b is 10 T m. If the side length of the square is tripled to 3b, the total length of the loop is also tripled. Therefore, the line integral of the magnetic field around the loop should also triple.
So, if the line integral was 10 T m for a loop of length b, it should be 30 T m for a loop of length 3b.
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