Next, a particle with the same mass and velocity as the...

Next, a particle with the same mass and velocity as the particle in Figure P24.59 enters the velocity selector. This particle has a charge of $2 q-$ twice the charge of the particle in Figure P24.59. In this case, we can say that. A. The force of the electric field on the particle is greater than the force of the magnetic field. B. The force of the magnetic field on the particle is greater than the force of the electric field. C. The forces of the electric and magnetic fields on the particle are still equal.

Next, a particle with the same mass and velocity as the particle in Figure P24.59 enters the velocity selector. This particle has a charge of $2 q-$ twice the charge of the particle in Figure P24.59. In this case, we can say that.
A. The force of the electric field on the particle is greater than the force of the magnetic field.
B. The force of the magnetic field on the particle is greater than the force of the electric field.
C. The forces of the electric and magnetic fields on the particle are still equal.

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Key Concepts

Scaling of Forces with Charge

Both the electric and magnetic forces scale linearly with the magnitude of the particle's charge. Therefore, if a particle's charge is doubled, both forces are doubled, maintaining the balance condition (i.e., F_electric = F_magnetic) in a velocity selector configuration.

Magnetic Force

The magnetic force on a charged particle moving through a magnetic field is given by F = qvB when the velocity is perpendicular to the magnetic field. This force is velocity-dependent and always acts perpendicular to both the particle's velocity and the magnetic field direction.

Velocity Selector

A velocity selector is a device that uses perpendicular electric and magnetic fields to filter particles based solely on their speed. For a particle to pass through undeflected, the electric force must exactly cancel the magnetic force, establishing the condition v = E/B.

Electric Force

The electric force acting on a charged particle in an electric field is directly proportional to the charge and the field strength, defined by the equation F = qE. This force acts in the direction of the field for positive charges and opposite for negative charges.

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