An electron and a proton, moving side by side at the same speed, enter a 0.020-T magnetic field. The electron moves in a circular path of radius 7.0 mm. Describe the motion of the proton qualitatively and quantitatively

a. Radius of the proton (r) = 12.85m

b. Velocity of the proton = 24.62 × 10⁶ m/s

c. Periodic Time (T) = 3.22 × 10⁻⁶ s

Explanation:

The motion of a proton can be described quantitatively and qualitatively by finding the velocity of the proton, the periodic time and radius of the proton.

The first step is to find the Radius of the circular path.

We would derive this formula for Force

Force = mass × acceleration

Where acceleration = (velocity)²/ radius

Therefore

Force of a proton  = Force of an electron

(mass of a proton × (velocity)²)/radius of a proton = (mass of a electron × (velocity)²)/radius of a electron

Radius of a proton = (mass of a proton × radius of an electron) ÷ mass of and electron

Mass of a proton = 1.67 × 10⁻²⁷kg

Mass of an electron = 9.1 × 10⁻³¹kg

Radius of an electron = 7.0mm = 7.0 × 10m

Radius of a proton = ( 1.67 × 10⁻²⁷kg× 7.0 × 10⁻³m) ÷ 9.1 × 10⁻³¹kg

Radius of a proton = ( 1.67 × 10⁻²⁷kg × 7.0 × 10⁻³m) ÷ 9.1 × 10⁻³¹kg

Radius of a proton = 12.85m

b. Velocity of a proton =

v = (B × r × q) ÷ m

Where B = Magnetic Flux = 0.020T

r = radius of a proton = 12.85m

q = charge of a proton = 1.602 × 10⁻¹⁹ coulombs

m = mass of a proton = 1.67 × 10⁻²⁷kg

Velocity of a proton = ( 0.020T × 12.85m × 1.602 × 10⁻¹⁹c ) ÷ 1.67 × 10⁻²⁷kg

Velocity of a proton = 24.62 × 10⁶ m/s

c. Periodic Time(T) = (2πr) ÷ v

where r = radius of a proton = 12.85m

v = velocity of a proton = 24.62 × 10⁶ m/s

T = (2 × π × 12.85m) ÷ 24.62 × 10⁶ m/s

= 3.22 × 10⁻⁶ s

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