You're welcome!

Thanks for your question! If J was uniform, then in the region 0 < r < R, the current I(r) would be equal to J * pi * r^2. On the other hand, for r > R, the current I would be constant and equal to J * pi * R^2.

Electric current is defined as dq/dt. In this problem, there is no N.

The radius of the disk in this problem is R, not a.

You're welcome! Let me know if you have any questions.

Thanks for your question! Vector F and vector ds are parallel, so the angle between them is zero. The dot product calls for the cosine of the angle between the two vectors, which is where cos 0 comes from.

Thanks for your comment! Here, r is really r(t), which is a function of time. One could replace r with r_0 + vt (which requires the introduction of an intermediate variable, r_0). One should still get the same final result eventually. Note that the emf should be expressed in terms of the given variables, which does not include t. So this emf is the time-dependent emf, but the time dependency is hidden within r.

Thanks for asking! I multiplied both sides by h, and divided both sides by g * lambda.

@@let_s_do_physics Thank you so much professor

Thanks!

Thanks! 😃

My pleasure!

Hello, thanks for your message. These are not necessarily from a specific source, and they are typical introductory college-level problems. If there is a specific problem that you'd like to see the solution for, please let me know and I'll be happy to create a video for it.

Thanks for the feedback! I will post the derivations soon!

Thanks!

Right, in this problem J is not constant, and it is equal to alpha x r. Alpha is a given constant in the problem.

@@let_s_do_physics I asked why. Never mind...

@@kocavrancic5324 This is how the problem was originally designed.

Glad it was helpful!

Thanks, will do!

Yes of course! What topics in particular?

Of course!

Correct, thanks for the suggestion.

Of course!