Question

This problem set will look at why the magnetic balls rolled slowly down the metal surfaces...This scenario is slightly different, but makes the math easier!

A square loop is cut out of a thick sheet of aluminum. It is then placed so that the top half is in a uniform magnetic field B (say 1T), and allowed to fall under gravity. (The first part of this problem requires you to set up dimensions.)  

If the magnetic field is B, what is the current induced in the loop of Al (in terms of your dimensional variables, B, AND the resistivity of Al) as the plate falls? What direction is the current in the loop (note it will depend on the direction of the B field!)? Finally determine an expression for the terminal velocity of the loop in terms of resistivity and density of Al and the magnetic field B. (net force =0). Draw a clear diagram! Comment on the form..does your answer make sense?

Note the dimensions of the loop cancel out, so look up the values of resistivity and density of Al and determine the actual numbers in m/s (assume B=1T).  

What would happen if you cut a tiny slit in the ring, breaking the circuit?

What if the entire loop was under the same magnetic field?

If you are in mechanics you should answer this question as well...

Now apply Newton's second law where a is not 0. Solve this differential equation (a= dv/dt) to find the velocity of the loop as a function of time. What is the terminal velocity? How long does it take to reach 90% of the terminal velocity?

Answer 1

answered by: anonymous