Question

If you can build a cyclotron with twice the radius and with the magnetic field twice as strong, by what factor would the allowed maximum particle energy increase?

a. 2
b. 4
c. 8
d. 16

Answer 1

d. 16

Step-by-step explanation:

Let

Charge on particle=q and mass of particle=m

Radius=2r

Magnetic field=2B

We have to find by what factor the maximum kinetic energy of particle increases.

We know that

Maximum kinetic energy of particle is given by

`K_(max)=(q^2B^2r^2)/(2m)`

Substitute the values then we get

Maximum kinetic energy of particle =
`(q(2B)^2(2r)^2)/(2m)`

Maximum kinetic energy of particle =
`16\cdot (q^2B^2r^2)/(2m)`

Hence, the maximum kinetic energy of particle increase by 16 when radius is twice and magnetic field is twice strong.

Answer:d.1 6