Question

Why is a cathode ray deflected by a nearby electric charge or magnet?

Short answer

Cathode rays are deflected due to the interaction of charged electrons with electric and magnetic fields, experiencing forces that change their path.

Step-by-step solution

Understanding Cathode Rays and Magnetic Fields

Cathode rays are streams of electrons emitted from the cathode in a vacuum tube. Electrons are charged particles, and when charged particles move, they create a magnetic field around themselves.

Interaction with Electric Fields

When cathode rays pass near an electric charge, the electric field exerts a force on the electrons due to their charge. According to the formula \( F = qE \), where \( F \) is the force, \( q \) is the charge of the electron, and \( E \) is the electric field strength, this force causes the electron to accelerate and change direction.

Interaction with Magnetic Fields

Cathode rays are also deflected by a magnetic field. According to the Lorentz force law, a moving charge in a magnetic field experiences a force given by \( F = q(v \times B) \), where \( v \) is the velocity of the electron and \( B \) is the magnetic field. This force acts perpendicular to the velocity of the electron, causing it to deflect.

Direction of Deflection

The deflection direction of cathode rays can be determined by the right-hand rule for magnetic fields or the direction of the electric field lines for electric fields. A positive electric charge attracts the cathode rays, while a negative charge repels them. Similarly, the orientation of the magnetic field affects the deflection direction based on the hand rule.

Key concepts

Electric Field and Charged Particles

When discussing electric fields, it's essential to understand how they influence charged particles like electrons. Electrons, which make up cathode rays, carry a negative charge. Therefore, they interact with the electric fields around them. An electric field is a region where an electric force acts, produced by charged objects. This force can push or pull on other charges in the field.
When cathode rays pass through or near an electric field, they experience a force because of their charge. This force can be determined by using the formula:

• \( F = qE \)

Here, \( F \) is the force exerted on the electron, \( q \) is the charge of the electron (a constant since electrons all have the same charge), and \( E \) represents the electric field strength. The result? The cathode ray accelerates and alters direction, showing how electric fields cause deflection in charged particles like cathode rays.

Magnetic Fields and Electron Deflection

Magnetic fields have a fascinating ability to affect moving charged particles. Unlike electric fields, which act on both stationary and moving charges, magnetic fields only exert force on moving charges. Electrons, as part of the cathode ray, are deflected when they move within a magnetic field. This happens because the magnetic field influences the path of the moving charges.
A magnetic field applies force at a right angle to the direction of the electron's motion, which makes the electron take on a curved path rather than moving straight. The strength of the magnetic field and the speed of the electron play crucial roles in the extent of deflection. This interaction is fundamental in devices like cathode ray tubes, where controlling electron paths with magnetic fields is routine.

Lorentz Force Law

The behavior of charged particles in magnetic fields boils down to the Lorentz force law. This law describes how moving electrons, such as those in cathode rays, interact with both electric and magnetic fields. It is presented with the equation:

• \( F = q(v \times B) \)

In this formula, \( F \) is the Lorentz force, \( q \) is the electron's charge, \( v \) is the velocity of the electron, and \( B \) is the magnetic field. This force acts perpendicular to both the velocity of the electron and the direction of the magnetic field. This perpendicular nature causes the electron to deflect, leading to a change in its trajectory. Understanding this law is vital, as it provides a clear mathematical framework of how and why electrons move as they do under the influence of magnetic fields.

Right-Hand Rule for Magnetic Fields

The right-hand rule is a straightforward way to determine the direction of the force on a moving charge within a magnetic field. When dealing with charges, such as electrons in cathode rays, this visual aid helps predict how they will travel when exposed to external magnetic forces. Here's how to apply the right-hand rule:

• Point your thumb in the direction of the electron's velocity (in case of moving charges).
• Extend your fingers in the direction of the magnetic field lines.
• The palm of your hand then points in the direction of the force experienced by a positive charge. Since electrons are negatively charged, the force direction is opposite to the palm's direction.

This method is particularly useful for quickly understanding and visualizing forces at play without needing to analyze equations. It is a practical tool to accompany the mathematical descriptions given by the Lorentz force law.