Find induced emf (among other things) in this current + motion

[1MileCrash]

Homework Statement

Attached

Homework Equations

The Attempt at a Solution

I'm pretty confused about this one.

First, I thought that maybe the magnetic field's non uniformity didn't matter since the rate of change of flux was going to be the rate of change of area, but that's wrong.

So I thought I should do some kind of integral to figure out the magnetic field from the top to bottom "per unit area" but that doesn't even make sense.

So then I decided to find the magnetic flux by integrating B dA but that still doesn't make much sense to me.

What do I do?

And what does resistance have to do with it? Or is that for one of the lower questions?

 

[1MileCrash]

In the integral for B dA, can I write the equation for B (mu 0 * i / 2piR) and replace R with the area for that R and integrate? Does that work?

 

[1MileCrash]

But that still won't get me a function of t so that I can differentiate to find rate... and R is constant anyway.

Very confused now.

 

[1MileCrash]

Is it some kind of double integral?

 

[Nickie]

I would first clarify the context of this problem. Is it a physics problem related to electromagnetic induction, or is it a question in a different field? Based on the information provided, I would assume that this is a physics problem.

In order to find the induced emf, we need to use Faraday's law of electromagnetic induction, which states that the induced emf is equal to the negative rate of change of magnetic flux through a surface. In this case, the motion of the current will create a changing magnetic flux through the surface.

To solve this problem, we need to determine the direction of the magnetic field at each point along the path of the current. This can be done using the right hand rule, where the fingers represent the direction of the current and the thumb points in the direction of the magnetic field. Once we have the direction of the magnetic field, we can use the equation for magnetic flux, Φ = BAcosθ, where B is the magnetic field, A is the area, and θ is the angle between the magnetic field and the area vector.

Next, we need to determine the rate of change of magnetic flux. This can be done by taking the derivative of the magnetic flux with respect to time. This will give us the induced emf.

As for the other questions about resistance and non-uniformity of the magnetic field, these may be related to further calculations in this problem or they may be for different questions. It is important to read the entire problem carefully and determine which equations and information are relevant.

In summary, to find the induced emf in this current and motion problem, we need to use Faraday's law and the equation for magnetic flux. It is important to determine the direction of the magnetic field and the rate of change of magnetic flux in order to solve the problem accurately.