Conductive disc power dissipation in oscillating field

[Emspak]

Homework Statement

A disc of conductivity σ is in an axial magnetic field B = B₀cosωt

The disc has radius a and thickness s

Homework Equations

possibly dP/dv = JE (dot product of two vectors) but I have absolutely no clue if it is relevant or not.

I think J=σE might be relevant, but I have no idea.

The Attempt at a Solution

I really don't know where to begin with this. I know that P= I V but I am completely lost as to whether or not I am supposed to derive the potential difference from the magnetic field, or what. This should be a simple plug- and - chug problem, but I can't seem to figure out where to begin, and I am feeling stupid because this is the first one in the problem set. Am I supposed to derive the electric field from the B field?

 

[anathema]

your first step should be to carefully read and understand the problem statement. In this case, you are given a disc of conductivity σ in an axial magnetic field B = B0cosωt, with specified dimensions (radius a and thickness s). From this information, you can infer that the disc is likely made of a conducting material, and that it is being subjected to a time-varying magnetic field.

Next, you should try to identify any relevant equations or principles that you can apply to solve the problem. In this case, you correctly identified the equation J=σE as potentially relevant, as it relates the current density (J) to the electric field (E) and conductivity (σ). You also correctly identified the equation for power (P=IV), but you are unsure of how to apply it in this context.

To solve this problem, you will likely need to use a combination of these equations, as well as possibly others. Your goal is to determine the potential difference (V) across the disc, given the magnetic field and its dimensions. To do this, you will need to consider the relationship between the magnetic field, electric field, and current density. You may also need to consider the geometry of the disc and how it is oriented with respect to the magnetic field.

It may also be helpful to break the problem down into smaller steps and think about what is happening at each step. For example, you could consider the induced electric field within the disc due to the changing magnetic field, and then use that to determine the current density and ultimately the potential difference.

In summary, as a scientist, your approach should be to carefully read and understand the problem, identify relevant equations and principles, and then break the problem down into smaller steps to help guide your thinking and problem-solving process. Don't be afraid to ask for help or clarification if you are stuck, and remember that it's okay to feel unsure or confused at first – that's often a normal part of the problem-solving process!