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**[SOLVED] Monstrous electromagnetism question.**

## Homework Statement

A slope variable: thèta

Amount of coils: 10.

Cilinder:

Diameter D

Length L

Massa M

Magnetic field B.

The cilinder has 10 coils wrapped around it, in rectangular form (over the top and bottom of the cilinder). It is placed on a slope with slope thèta, and the coils are horizontal at first. The current goes in a counter-clockwise motion when looked upon from above. There is a magnetic field with strength B, which is perpendicular and upwards. We release the cilinder to all forces. Give the formula for the minimal amound of amps going through the coils to make sure it doesnt keep rolling downwards.

## Homework Equations

F=BIL(sinalpha)

F=mg

rot E = - dB/dt

## The Attempt at a Solution

Many attempts, many failed. I just had this question on an exam, and man this was a brain teaser. The flux varies sinoïdal due to the rotation of the cilinder. Hence causing an electromotoric force. On the other side, we must find a minimal current to go through the coils, so that when the force pair of the lorentzforce on the coils is strong enough to fight the gravitational force of rolling downwards. This however, can't be at the first moment, because we place the coils horizontally, hence meaning that the force pair cancels eachother out and has no tangential component. Once it begins rotating, it gathers momentum, so we must find a current, so that it cancels out the gravitational force, and it has enough time to reduce the angular speed to zero and reverse it. We also know that the law of faraday states that the amps are influence by the fluctuating magnetic flux through the coils. Hence creating a fluctuating voltage. This will however turn around in signum after rolling 90 degrees, hence it is (IM NOT SURE ABOUT THIS) that the reversal must happen in the first quadrant.

Any idea's on how to solve this monstrous question?