Ampere's Law and Choosing a Loop for Integration

[Marcin H]

Homework Statement

Homework Equations

Amperes law

The Attempt at a Solution

This is a solution to an old exam and I am confused by the application of amperes law here.
What is the general rule for drawing our "ampere'ian surface" when using amperes law? I thought we have to draw a countour that encloses I and have it in the direction of the bfield created by I

For example, in this question, I don't understand why they drew the contour around the bottom plate like that and in the zx plane. Why is the contour like that? And why is the integral of dl just equal to w? I thought we had to sum the length of the contour. For example if the contour was a circle we would say integral of dl is 2(pi)r.

 

[kuruman]

Rule 1: Choose your loop so that current flows through it.
Rule 2: Verify by using a symmetry argument that the B-field is constant on the entire loop and has direction either perpendicular or parallel to the loop (sense of integration).

In this example you can draw the loop either around the bottom plate or the top to satisfy Rule 1. If you draw it around both plates you get zero net current through which by the way says that B-field is zero outside the plates. The symmetry argument is supported by the given "Assume that ... " wording. The integral is Bw because
B⋅dl = B dl since B and dl are in the same direction. Take B out of the integral because it is the same every where between the plates and you have the integral of dl. What is that?

 

[PumpkinCougar95]

You can refer to : https://www.physicsforums.com/threads/magnetic-field-of-an-infinite-sheet-of-current.475918/

 

[Marcin H]

Rule 1: Choose your loop so that current flows through it.
Rule 2: Verify by using a symmetry argument that the B-field is constant on the entire loop and has direction either perpendicular or parallel to the loop (sense of integration).

In this example you can draw the loop either around the bottom plate or the top to satisfy Rule 1. If you draw it around both plates you get zero net current through which by the way says that B-field is zero outside the plates. The symmetry argument is supported by the given "Assume that ... " wording. The integral is Bw because
B⋅dl = B dl since B and dl are in the same direction. Take B out of the integral because it is the same every where between the plates and you have the integral of dl. What is that?

got it. thanks