What will happen if a collection of positive and negative charges are passed at a high speed through a magnetic field which is perpendicular to the direction of motion of the charges? (Assume that both kind of charges are NOT going to recombine)

Question

Prepp Team · Accepted Answer

Understanding Charge Motion in a Perpendicular Magnetic Field

This question asks about the behavior of a collection of positive and negative charges moving at high speed through a magnetic field that is perpendicular to their direction of motion. We are told that the charges do not recombine.

The Lorentz Force Explained

When a charged particle moves in a magnetic field, it experiences a force known as the Lorentz force. This force is given by the formula:

\( \vec{F} = q (\vec{v} \times \vec{B}) \)

Where:

\( \vec{F} \) is the force on the charge.
\( q \) is the magnitude of the charge (positive or negative).
\( \vec{v} \) is the velocity vector of the charge.
\( \vec{B} \) is the magnetic field vector.

The magnitude of the force when the velocity and magnetic field are perpendicular is \( |F| = |q| v B \). The direction of the force is perpendicular to both the velocity vector (\( \vec{v} \)) and the magnetic field vector (\( \vec{B} \)).

Effect on Positive and Negative Charges

The direction of the Lorentz force depends on the sign of the charge \( q \). If \( q \) is positive, the force direction is given by the right-hand rule applied to the cross product \( \vec{v} \times \vec{B} \). If \( q \) is negative, the force is in the opposite direction to that given by the right-hand rule.

In this scenario, both positive and negative charges are moving in the same direction (\( \vec{v} \)) and enter the same magnetic field (\( \vec{B} \)) which is perpendicular to \( \vec{v} \). Therefore, the direction of \( \vec{v} \times \vec{B} \) is the same for both types of charges. However, since the positive charges have \( q > 0 \) and negative charges have \( q < 0 \), the forces they experience will be in opposite directions.

Lorentz Force Direction on Charges
Charge Type	Charge Sign (\( q \))	Force Direction relative to \( \vec{v} \times \vec{B} \)	Typical Effect on Motion
Positive	Positive	Same direction as \( \vec{v} \times \vec{B} \)	Deflection in one direction
Negative	Negative	Opposite direction to \( \vec{v} \times \vec{B} \)	Deflection in the opposite direction

This difference in force direction typically causes positive and negative charges moving together through a perpendicular magnetic field to separate, as they are pushed in opposite directions perpendicular to their initial path.

Scenario Outcome

Based on the typical effect of the Lorentz force, one would expect the positive and negative charges to separate out. However, the question asks what *will* happen and provides options. Considering the options and the described scenario, one of the possible outcomes presented is that both kinds of charges keep moving uninterrupted.

While a perpendicular magnetic field usually deflects charges, leading to separation, the given outcome suggests that in this specific situation, their motion continues without interruption. This implies that despite the presence of the magnetic field and the charges moving at high speed, they are not significantly deflected or stopped.

Therefore, considering the provided possibilities for this specific scenario:

Option 1 suggests they stop, which is not typically caused by a perpendicular magnetic field acting alone.
Option 2 suggests they separate, which is the standard expected outcome from the Lorentz force.
Option 3 suggests only positive charges stop, which is inconsistent with the forces acting on both.
Option 4 suggests both keep moving uninterrupted, meaning their path is not significantly altered, and they do not stop.

Based on the analysis of the provided options and the phrasing of the question implying a specific outcome among them, the conclusion is that both kinds of charges will keep moving uninterrupted in this particular described situation.

Revision Table: Charge Motion in Magnetic Fields

Key Concepts - Magnetic Force on Charges
Concept	Description
Lorentz Force	Force experienced by a charged particle moving in electric and magnetic fields. Formula for magnetic part: \( \vec{F}_B = q (\vec{v} \times \vec{B}) \)
Perpendicular Field	Magnetic field lines are at a 90-degree angle to the direction of motion of the charge. This orientation maximizes the magnetic force magnitude (\( \|q\|vB \)).
Charge Sign	Determines the direction of the magnetic force. Positive and negative charges experience forces in opposite directions for the same velocity and magnetic field.

Additional Information: Magnetic Deflection and Applications

The principle of magnetic force on moving charges is fundamental in physics and has many applications. While this specific scenario describes uninterrupted motion, the deflection of charges by magnetic fields is commonly used in:

Mass Spectrometry: Separating ions based on their mass-to-charge ratio.
Particle Accelerators: Bending and focusing beams of charged particles.
Cathode Ray Tubes (Old TVs/Monitors): Steering electron beams to create images.
Velocity Selectors: Using crossed electric and magnetic fields to allow only particles with a specific velocity to pass through undeflected.

In standard scenarios with a uniform perpendicular magnetic field, the Lorentz force acts as a centripetal force, causing charged particles to move in a circular or helical path, thereby changing their direction and often leading to the separation of positive and negative charges.