Answer:
24 cm
Explanation:
Given:
Mass of proton = 1.67 × 10⁻²⁷ Kg
kinetic energy = 2.5 × 10⁻¹³ J
magnetic field in the cyclotron, B = 0.75 T
Now,
Kinetic energy = = 2.5 × 10⁻¹³ J
where, v is the velocity of the electron
or
= 2.5 × 10⁻¹³ J
or
v² = 2.99 × 10¹⁴
or
v = 1.73 × 10⁷ m/s
also,
centripetal force = magnetic force
or
= qvB
q is the charge of the electron
r is the radius of the dipole magnets
on substituting the respective values, we get
= 1.6 × 10⁻¹⁹ × 0.75
or
r = 0.2408 m ≈ 24 cm
Hence, the correct answer is 24 cm