A beam of protons enters a uniform magnetic field of0.3T with velocity of4 × 105m/sin a direction making an angle of 60° with the direction of magnetic field, the pitch of the helix (inmetres) will be :Correct answer is '0.0437'. Can you explain this answer?

Question

A beam of protons enters a uniform magnetic field of0.3T with velocity of4 &times; 105m/sin a direction making an angle of 60&deg; with the direction of magnetic field, the pitch of the helix (inmetres) will be :Correct answer is '0.0437'. Can you explain this answer?

Answer

In order to determine the effect of the magnetic field on the protons, we need to use the formula for the magnetic force on a charged particle:

F = qvB sinθ

Where:
F = magnetic force on the proton (in Newtons)
q = charge of the proton (in Coulombs)
v = velocity of the proton (in meters per second)
B = magnetic field strength (in Tesla)
θ = angle between the velocity vector and the magnetic field vector (in degrees)

Since the protons have a positive charge and are moving perpendicular to the magnetic field, the angle θ is 90 degrees. Therefore, sinθ = 1.

Assuming the charge of the proton is 1.6 x 10^-19 Coulombs, and the velocity is 4 x 10^6 meters per second, we can calculate the magnetic force:

F = (1.6 x 10^-19 C)(4 x 10^6 m/s)(0.3 T)(1)

F = 1.92 x 10^-13 N

So, the magnetic force on the protons is 1.92 x 10^-13 Newtons.

Answer

The correct answer is: 0.0437

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