[Lolicakes]

Just trying to work out a question from my book, all help is appreciated.

A 30cm radius cyclotron has a magnetic field of about 0.5T. Estimate the energy in MeV gained by accelerated protons.

The answer given in the book is 1.08.

[teachercol]

More info needed.

[Fleming92]

Ok, so first assume that protons will be moving in a perfect circular motion. (After all they are in a cyclotron :P)

Then we can equate the centripital force due to the magnetic field, qvB, to that of the force of cicular motion from mechanics, ie F= (mv^2)/r

equating these two expressions, alows you to cancel a v (velocity) from each side. After which you can re-arrange to get a value for v.

(I got 1.437 x 10^ 7 m/s)

Then simply put into the equation for kinetic energy, 1/2 m v^2 to get and enegry value in J.

Then simply convert to MeV!

[teachercol]

Seems reasonable.