9.03 x 10³ m /s
Explanation:
magnetic field inside a solenoid
B = μ₀ n I , where μ₀ = 4π X 10⁻⁷ .
n is no of turns per unit length and I is current
so B₁ = 4π x10⁻⁷x 593 / 20.9 x 5.65 x 10²
201.5 x 10⁻⁴ T
B₂ = 4π x 10⁻⁷ x 343 / 19.1 x 1.37 x 10²
= 30.93 x 10⁻⁴ T
Net magnetc field
B₁ -B₂ = B = (201.5 - 30.93) x 10⁻⁴ T
B = 170.57 x 10⁻⁴ T
Now protons move in circular path of radius R in the magnetic field of B
B q v = m v² / R
v = B q R / m
= 170 .57 x 10⁻⁴ x 1.6 x 10⁻¹⁹ x 5.53 x 10⁻³ / (1.67 x 10⁻²⁷)
= 903.71 x 10
= 9.03 x 10³ m /s
=