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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 :

lublana

Answer:

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=[tex]\frac{1}{2}\frac{q^2B^2r^2}{m}[/tex]

Substitute radius= 2r

Then, maximum kinetic energy of particle =[tex]\frac{q^2B^2(2r)^2}{2m}=4\frac{q^2B^2r^2}{2m}=4\cdot K.E_{max}[/tex]

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

Answer: b.4

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