The magnetic force on a charged moving particle A. depends...

The magnetic force on a charged moving particle A. depends on the sign of the charge on the particle. B. depends on the magnetic field at the particle's instantaneous position. C. is in the direction which is mutually perpendicular to the direction of motion of the charge and the direction of the magnetic field. D. is proportional both to the charge and to the magnitude of the magnetic field. E. is described by all of the above options, A through D.

The magnetic force on a charged moving particle
A. depends on the sign of the charge on the particle.
B. depends on the magnetic field at the particle's instantaneous position.
C. is in the direction which is mutually perpendicular to the direction of motion of the charge and the direction of the magnetic field.
D. is proportional both to the charge and to the magnitude of the magnetic field.
E. is described by all of the above options, A through D.

Key Concepts

Lorentz Force

The Lorentz force is the fundamental principle that describes the force exerted on a charged particle due to electromagnetic fields. It states that a particle with charge q moving with velocity v in a magnetic field B experiences a force given by F = q (v × B). This formulation encapsulates dependencies on the charge’s magnitude, its sign, and the magnetic field’s strength and direction.

Magnetic Field

The magnetic field is a vector field that represents the influence exerted on moving charges and magnetic dipoles. Its magnitude and direction at any given point determine how a charged particle moving through it will be affected, particularly in terms of the force’s magnitude and orientation.

Vector Cross Product

The vector cross product is a mathematical operation used to determine the direction and magnitude of the magnetic force acting on a moving charge. Because the cross product of two vectors results in a vector perpendicular to both, it explains why the magnetic force is perpendicular to both the velocity of the particle and the direction of the magnetic field.

Charge (Sign and Magnitude)

The charge of a particle plays a crucial role in determining the magnetic force acting on it. The magnitude of the charge directly scales the force, while the sign of the charge affects the direction of the force, effectively reversing it when the charge is negative.

Right-Hand Rule

The right-hand rule is a common mnemonic used to determine the direction of the magnetic force on a positively charged particle. By pointing the fingers of the right hand along the particle’s velocity and curling them toward the magnetic field, the thumb indicates the direction of the force. For negatively charged particles, the force direction is opposite.

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