Question

A beam of protons with speed 4 × 10⁵ ms^-1 enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to :

(Mass of the proton = 1.67 × 10^-27 kg, charge of the proton = 1.69 × 10^-19 C)

Options

• 12 cm

• 2 cm

• 4 cm

• 5 cm

Answer 1

4 cm

Explanation:

Given: Speed of beam of protons is v = 4 × 10⁵ m/s, the protons enter a uniform magnetic field with magnitude B = 0.3 T, angle between v and B is θ = 60°, mass of proton is m = 1.67 × 10^-27 kg, charge on proton is e = 1.6 × 10^-19 C.

To find: p, the pitch of the helical path followed by the protons.

Let T be the time period of proton's motion in the magnetic field.

p = v cos θ × T

p = v cos θ × `(2pi"m")/"eB"`

= 4 cm.