This lesson explains how a uniform magnetic field bends the path of a charged particle moving perpendicular to the field. The magnetic force can act as a centripetal force, producing circular motion without changing the particle’s speed.
A moving charged particle in a magnetic field experiences a magnetic force. Its magnitude is FB=∣q∣vBsinθ, where q is the particle’s charge, v is its speed, B is the field strength, and θ is the angle between velocity and the magnetic field.
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What force maintains circular motion when a charged particle moves perpendicular to a uniform magnetic field?
The magnetic force acts as the centripetal force, continually directing the particle toward the circle’s center.
What determines the radius of a charged particle’s circular path in a uniform magnetic field?
For perpendicular motion, r=mv/(∣q∣B); the radius depends on mass, speed, charge magnitude, and field strength.
What is the period of a charged particle’s circular motion in a uniform magnetic field?
The time for one revolution is T=2πm/(∣q∣B), independent of speed.
How does an obliquely moving charged particle form a helix in a uniform magnetic field?
Its perpendicular velocity component produces circular motion while its parallel component carries it along the field.
What is the pitch of a charged particle’s helical path?
The distance along the magnetic field between successive turns; p=v∥T.
Quiz questions
For a fixed particle in a uniform magnetic field, how does the period of circular motion depend on speed?Answer: The period is independent of the particle’s speed.
For a negative charge moving in a magnetic field, how does the force direction compare with the right-hand-rule direction?Answer: The force points opposite to the right-hand-rule direction.
What makes a magnetic bottle confine a charged particle?Answer: The particle is reflected at both ends of the region.
How do energetic charged particles produce auroral light in a planet’s atmosphere?Answer: Collisions excite atmospheric atoms and molecules, which emit light as they return to lower-energy states.
Which velocity component determines the radius of a charged particle’s helical path?Answer: The component perpendicular to the magnetic field.
Based on University Physics Volume 2 by Samuel J. Ling, William Moebs, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.