The line integral is Ihe same for all three loops shown below. Loops 1 and 2 hav

Question

The line integral is Ihe same for all three loops shown below. Loops 1 and 2 have the same perimeter. Consider following discussion about the incorrect predictions made by three Student Student 1: "It seems like the integral around Loop 2 should be greater. They're the same length, but in Loop 2 the magnetic field always points along the path, and in Loop 1 only a component of the magnetic field points along the path" Student 2: "I thought that Loop 3 should be the largest integral, since the loop is closest to the wire so the magnetic field is strongest." Student 3: "I predicted the opposite. The path is shorter around Loop 3, so the integral around Loop 3 should be less than that around Loop 2." Explain why each student's prediction is incorrect.

Explanation / Answer

from Ampere's Law,

Integral of B.dL = u0 I

1: Integral will be same becuase.

I (current inside) is same for both loops. (u0 is constant )

hence u0 I will be same for both loops so is integral.

2: same explanation as give to 1.

integral doesn't depends on length of permieter.

it depends only and only on current inclosed.

hence integral will be same.

3: As explained. Integral will be same.

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