Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A charge particle moves in a region having a uniform magnetic field and a parallel, uniform electric field. At some instant, the velocity of the particle is perpendicular to the field direction. The path of the particle will be
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Understand the forces acting on the charged particle. The particle experiences a magnetic force given by \( \mathbf{F}_B = q(\mathbf{v} \times \mathbf{B}) \) and an electric force given by \( \mathbf{F}_E = q\mathbf{E} \).
Step 2: When the velocity of the particle is perpendicular to the magnetic field, the magnetic force will act perpendicular to both the velocity and the magnetic field. This results in circular motion if there were only a magnetic field acting on the particle. However, a uniform electric field is also present, which provides a constant force in a specific direction (along the field lines).
Step 3: The magnetic force does not do work on the particle since it is always perpendicular to the velocity, and thus, does not change the speed, only the direction. The electric field provides a constant acceleration that affects the velocity's direction but not its magnitude.
Step 4: As the electric field continuously shifts the velocity direction while also having a constant speed (because of magnetic field), the particle moves forward in the direction of the electric field while executing circular motion due to the magnetic field. This results in a straight-line path when viewed from a suitable frame.
Step 5: Conclusion: The combined effect leads to a straight path due to the constant forward motion from the electric field with varying direction from the magnetic field.
Therefore, the correct answer is a straight line.
Step 2: When the velocity of the particle is perpendicular to the magnetic field, the magnetic force will act perpendicular to both the velocity and the magnetic field. This results in circular motion if there were only a magnetic field acting on the particle. However, a uniform electric field is also present, which provides a constant force in a specific direction (along the field lines).
Step 3: The magnetic force does not do work on the particle since it is always perpendicular to the velocity, and thus, does not change the speed, only the direction. The electric field provides a constant acceleration that affects the velocity's direction but not its magnitude.
Step 4: As the electric field continuously shifts the velocity direction while also having a constant speed (because of magnetic field), the particle moves forward in the direction of the electric field while executing circular motion due to the magnetic field. This results in a straight-line path when viewed from a suitable frame.
Step 5: Conclusion: The combined effect leads to a straight path due to the constant forward motion from the electric field with varying direction from the magnetic field.
Therefore, the correct answer is a straight line.
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