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I'm confused about the premise of this homework problem:

A thin, non-conducting horizontal disc lies in the $x$-$y$ plane. The disc has a mass $m$ and a total charge $q$ distributed uniformly over its surface. The disc can freely rotate about its axis.
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The disc is initially stationary. Then, at time $t=0 ,$ a magnetic field $\vec{B}$ directed in the direction of the $z$-axis (so perpendicular to the disc's plane) is switched on.

Problem: Find the disc's angular velocity $\omega \left( t \right)$ as function of time, assuming that $\mathrm{B}=kt ,$ where $t$ is time.

This problem implies that the magnetic field, $\vec{B} ,$ causes a torque, making the disc rotate. However, I don't understand how the magnetic field would cause the disc to rotate at all.

I have studied electromagnetic induction, and I know that an electromotive force (emf) will be generated due to the change in magnetic flux. But, how will this emf help this disc to rotate?

Question: How does the magnetic field perpendicular to the disc cause it to rotate?

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  • $\begingroup$ Please give me suggestion what should I do to improve my question. Any specific reason to down vote this question? $\endgroup$ – jayant98 Feb 3 at 12:43
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    $\begingroup$ This looks very much like a "how do I solve this problem" question which is considered off-topic here, hence the downvotes. $\endgroup$ – Kyle Kanos Feb 3 at 13:34
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    $\begingroup$ @Kyle But, I am only asking about which torque operates and how? Not asking people to solve the numerical for me. Just about the torque and its working. $\endgroup$ – jayant98 Feb 3 at 13:36
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    $\begingroup$ If that is your interest, I think you need to edit the question to remove the "this is my homework, what do I do next" aspect and focus on the conceptual question you want to ask. $\endgroup$ – Kyle Kanos Feb 3 at 13:44
  • $\begingroup$ @Kyle Please see if now it is okay to ask? $\endgroup$ – jayant98 Feb 3 at 13:52
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In principle, electromagnetic induction is about the existence of an electric field with non-conservative circulation.

This electric field can generate a current in a closed circuit, that is to say to make charges turn !

In your case, you must first look for the electric field associated with the variable magnetic field and then look at how this electric field acts on the charged disk.

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Your knowledge of e-m induction will have enabled you to find the emf around a circle of radius r on the disc. That means you know know much work per coulomb would be done on a test charge taken around that circle. But you know what work means, so you can calculate the force per unit charge on your test charge. What do we call this?

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