Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A beam of protons enters a uniform magnetic field of 0.3T with velocity of 4 × 10 5 m/s in a direction making an angle of 60º with the direction of magnetic field. The path of motion of the particle will be
Text Solution
Verified by ExpertsThe correct answer is:
D
Step 1: Understand the motion of charged particles in a magnetic field. When a charged particle, such as a proton, enters a magnetic field at an angle, it experiences a magnetic force given by the Lorentz force equation:
F = q(v × B),
where q is the charge of the proton, v is its velocity, and B is the magnetic field.
Step 2: Determine the components of velocity. The velocity can be resolved into two components relative to the magnetic field:
- v_perpendicular (perpendicular to B)
- v_parallel (parallel to B)
The component perpendicular to the magnetic field will cause circular motion, while the component parallel will result in linear motion along the field lines.
Step 3: In this case, since the proton enters at an angle of 60º, both components are present:
v_perpendicular = v imes sin(60°)
v_parallel = v imes cos(60°)
Step 4: The perpendicular component results in circular motion (due to the magnetic force), while the parallel component causes the proton to move along the direction of the magnetic field line. This results in a helical trajectory.
Conclusion: Therefore, the overall path of the proton is helical as it moves through the magnetic field.
Therefore, the correct answer is D.
F = q(v × B),
where q is the charge of the proton, v is its velocity, and B is the magnetic field.
Step 2: Determine the components of velocity. The velocity can be resolved into two components relative to the magnetic field:
- v_perpendicular (perpendicular to B)
- v_parallel (parallel to B)
The component perpendicular to the magnetic field will cause circular motion, while the component parallel will result in linear motion along the field lines.
Step 3: In this case, since the proton enters at an angle of 60º, both components are present:
v_perpendicular = v imes sin(60°)
v_parallel = v imes cos(60°)
Step 4: The perpendicular component results in circular motion (due to the magnetic force), while the parallel component causes the proton to move along the direction of the magnetic field line. This results in a helical trajectory.
Conclusion: Therefore, the overall path of the proton is helical as it moves through the magnetic field.
Therefore, the correct answer is D.
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