Which of the following choices of path allow you to use Ampère’s law to find B(r).

1. The path must pass through the point r_vec.
2. The path must have enough symmetry so that B(r)x dl is constant along large parts of it.
3. The path must be a circle.
choices are....

a only
a and b
a and c
b and c

You can use amperes closed form integral on ANY closed path. To get B, the current has to pass through the surface formed by the closed path.

Now, I don't like the answers. THe question is which choices of path allow you to ...

Then all the answers say path MUST....
a) I have no idea what rvec means, without some graphical reference.
b) The path does not have to have any symetry, but it is nice if it does. In either case, you are allowed to choose any path which encloses the current.
c) The path does not have to be a circle, but it is nice if it does.

Did a Graduate Student write this test question?

no its a website. and that last choice doesnt make sense cause it asks which allows and that sats it must be...so is that one right? and the r_vec is is some point in the field.

The correct answer is option a - "The path must pass through the point r_vec."

In order to use Ampère's law to find B(r), the path must pass through the specific point r_vec where you want to determine the magnetic field. Ampère's law relates the magnetic field along a closed loop to the current enclosed by that loop, and the path chosen must enclose the desired point of interest in order to accurately calculate B(r).

Based on the given choices, the correct answer is (a) only.

To understand why, let's review Ampère's law and the conditions required to use it to find B(r).

Ampère's law relates the magnetic field (B) along a closed loop to the electric current (I) passing through the loop. It states that the line integral of the magnetic field around a closed path (known as the Ampèrean loop) is equal to μ₀ times the total electric current passing through the loop, where μ₀ is the permeability of free space.

In order to use Ampère's law to find B(r) at a specific point r, we need to choose a path that satisfies certain conditions:

1. The path must pass through the point r_vec: This condition is necessary because we want to determine the magnetic field at that specific location. Therefore, any path that does not pass through r_vec will not give us the desired information.

2. The path must have enough symmetry so that B(r) x dl is constant along large parts of it: This condition is important because it allows us to simplify the integration over the path. If B(r) x dl is constant along large parts of the path, then we can move it outside the integral sign, which greatly simplifies the calculation. Note that this condition does not imply that the path must be symmetric, but rather that it must have sufficient symmetry in relation to the magnetic field.

3. The path must be a circle: This condition is not necessary to apply Ampère's law. While a circular path is often used because of its simplicity and symmetry, it is not a requirement. Ampère's law can be used as long as the chosen path satisfies the conditions mentioned above.

In light of these explanations, the only choice that satisfies the first condition (the path passes through r_vec) is choice (a) only. Thus, the correct answer is (a) only.