A beam of protons with velocity 4 × 105 m / s enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. Find the radius of the helical path taken by the proton beam.

Question

A beam of protons with velocity 4 × 105 m / s enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. Find the radius of the helical path taken by the proton beam. (A) 0.2 cm (B) 1.2 cm (C) 2.2 cm (D) 0.122 cm

Tardigrade Admin · Accepted Answer

When the charged particle is moving at an angle to the field (other than

0^{\circ}, 9 0^{\circ}

and

18 0^{\circ}

),
in this situation resolving the velocity of the particle along and perpendicular to the field, we find that the particle moves with constant velocity

v cos θ

along the field and at the same time it is also moving with velocity

v sin 6

perpendicular to the field due to which it will describe a circle (in a plane perpendicular to the field) of radius

r = \frac{m ( v s i n θ )}{qB}

Here,

m = 1.67 \times 1 0^{- 27} k g

v = 4 \times 1 0^{5} m / s

θ = 6 0^{\circ}

q = 1.6 \times 1 0^{- 19} C

B = 0.3 T

∴ r = \frac{1.67 \times 1 0 ^{- 27} \times 4 \times 1 0 ^{5} \times ( 3 /2 )}{1.6 \times 1 0 ^{- 19} \times 0.3}

= 0.012 m

= 1.2 c m

Q. A beam of protons with velocity 4×105m/s enters a uniform magnetic field of 0.3T at an angle of 60∘ to the magnetic field. Find the radius of the helical path taken by the proton beam.

0.2 cm

1.2 cm

2.2 cm

0.122 cm

Q. A beam of protons with velocity $4 \times 1 0^{5} m / s$ enters a uniform magnetic field of $0.3 T$ at an angle of $6 0^{\circ}$ to the magnetic field. Find the radius of the helical path taken by the proton beam.