If you can build a cyclotron with twice the radius, by what factor would the allowed maximum particle energy increase? assume that the magnetic field remains the same.
a. 2
b. 4
c. 8
d. 16

b.4

Explanation:

Let

Magnetic field produced=B

Charge on particle=q

Mass of charged particle=m

Radius=2r

We have to find the k.E of the particle   by what factor increases when radius taken twice .

Maximum K.E of particle in cyclotron=

Substitute radius= 2r

Then, maximum kinetic energy of particle =

Hence, the maximum kinetic energy of the particle increases by 4 when radius taken twice.

b.4

it is easily magnetized.