Question

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

Answer 1

b.4

Step-by-step 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=
`(1)/(2)(q^2B^2r^2)/(m)`

Substitute radius= 2r

Then, maximum kinetic energy of particle =
`(q^2B^2(2r)^2)/(2m)=4(q^2B^2r^2)/(2m)=4\cdot K.E_(max)`

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

Answer: b.4