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Chapter 15: Problem 39

A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a (A) Straight line (B) Circle (C) Helix (D) Cycloid

Short Answer

Expert verified
The charged particle will move in a helix path (C) due to the combined effects of both the electric and magnetic fields. The electric field will cause a constant acceleration in the direction of the field, while the magnetic field creates a circular motion due to its force being perpendicular to the particle's velocity. This combination results in a helical motion.

Step by step solution

01

Electric Field Effect

Because the electric field is uniform and the particle has an initial velocity of zero, the electric force (\( qE \)) exerted on the particle will cause it to accelerate in the direction of the electric field. The acceleration will be constant and linear throughout the motion of the particle due to the uniformity of the field.
02

Magnetic Field Effect

When the charged particle starts moving under the influence of the electric field, it will also experience a force due to the magnetic field. The magnetic force (\(q(vB \sin{\theta})\)) depends on the speed of the particle (\(v\)), the magnetic field strength (\(B\)), and the angle (\(\theta\)) between the velocity vector and the magnetic field direction. Since both fields are parallel, \(\theta = 0\), which implies the magnetic force will be zero when the particle starts moving. However, as the particle accelerates in the direction of the electric field, it will gain a component of velocity perpendicular to the magnetic field direction. Then, the particle will experience a magnetic force that is always perpendicular to its velocity. This magnetic force will cause the charged particle to move in a circular motion. The radius of the circle depends on the particle's mass, charge, and velocities.
03

Combining Electric and Magnetic Field Effects

The constant acceleration from the electric field causes the particle to move in a linear direction, while the magnetic force makes it travel in a circular path. These two motions combine to form a helical motion or helix. Thus, the answer is: (C) Helix

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