Question

The accompanying figures show a cathode-ray tube (figure A) and the deflection of an electron in a region of magnetic field (figure B). If deflection in the tube is being produced by the magnetic field alone, predict the effect on the observed deflection by increasing (a) mass of particles, (b) velocity of the particles, (c) magnetic field, and (d) charge on the

Short answer

In summary, the effect of increasing each factor on the observed deflection in the cathode-ray tube is as follows: (a) Mass of particles: Increasing the mass will cause the observed deflection to decrease. (b) Velocity of particles: Increasing the velocity will cause the observed deflection to increase. (c) Magnetic field: Increasing the magnetic field will cause the observed deflection to increase. (d) Charge on the particles: Increasing the charge will cause the observed deflection to increase.

Step-by-step solution

Lorentz Force Equation

First, we'll apply the Lorentz Force equation mentioned above to find out the force acting on the charged particles in the magnetic field. The equation is: \[F = q(v \times B)\]

Effect of mass of particles

When the mass of the particles is increased, their motion under the influence of the magnetic field is affected according to Newton's second law: \[F = m \times a\] where \(m\) is the mass of the particle and \(a\) is the acceleration. Since the mass is increased and the force from the magnetic field remains constant, the acceleration will decrease. This means that there will be less deflection observed than before. So, the effect of increasing the mass of particles on the observed deflection is that it will decrease.

Effect of velocity of particles

According to the Lorentz force equation, increasing the velocity of the particles increases the force acting on them. However, increasing the velocity also decreases the time the particles spend within the magnetic field region. Since both factors have opposite effects on the observed deflection, we need to consider their net effect. Mathematically, the net force acting on the particles is increased, thus, increasing the observed deflection. Thus, the effect of increasing the velocity of particles on the observed deflection is that it will increase.

Effect of magnetic field

When the magnetic field is increased, the force acting on the charged particles (according to the Lorentz force equation) is also increased. This increased force will cause a larger deflection of the particles, all other factors remaining constant. So, the effect of increasing the magnetic field on the observed deflection is that it will increase.

Effect of charge on the particles

As stated in the Lorentz force equation, the force acting on the particles is directly proportional to their charge. If we increase the charge on the particles, the force on them will also increase, and hence, the observed deflection will increase. Thus, the effect of increasing the charge on the particles on the observed deflection is that it will increase.

Key concepts

Cathode-ray Tube

A cathode-ray tube (CRT) is a device used primarily in older television and computer display systems. It works by emitting electron beams from a cathode and projecting them onto a fluorescent screen. The CRT consists of several main parts: the electron gun, where electrons are generated; the deflection system, which steers the electron beam; and the phosphorescent screen, where the image is displayed.

Electrons emitted from the cathode are accelerated and focused into a beam. This beam is directed and deflected by electric or magnetic fields. The position on the screen where the beam strikes determines the visual output. The interactions between charged particles, like electrons, and magnetic fields are crucial in changing the beam’s path, enabling it to display images.

Without the manipulation of electron paths, the screen would not be able to dynamically display complex images. Understanding how electron beams can be controlled involves fundamental concepts of physics, such as Lorentz force and particle motion.

Magnetic Field

A magnetic field is a region around a magnetic material or a moving electric charge within which the force of magnetism acts. Magnetism can attract or repel objects. It plays a crucial role in influencing the movement of charged particles, such as electrons in a cathode-ray tube.

The strength and direction of a magnetic field are typically represented by magnetic field lines. These lines indicate the direction of the magnetic force at different points in the field. In the case of electron beams in a CRT, the magnetic field lines show the path along which the electrons will be deflected.

Lorentz force governs the interaction between a charged particle moving in a magnetic field. When an electron, with velocity **v**, moves through a magnetic field, the magnetic force acting upon it can be expressed as \( F = q(v \times B) \), where \( q \) is the charge and \( B \) is the magnetic field intensity. The cross-product indicates that the force is perpendicular to both the velocity and the magnetic field.

• Increased magnetic field strength increases the force on charged particles.
• This results in a larger deflection of particles.

This principle allows the CRT to manipulate electron paths and form images based on magnetic interactions.

Newton's Second Law

Newton's Second Law of Motion is fundamental in understanding the movement of particles under force. It states that the force acting on an object is equal to the mass of the object multiplied by its acceleration, mathematically expressed as \( F = m \times a \).

In the context of a cathode-ray tube, Newton's Second Law helps explain the deflection of electron beams in a magnetic field. When a magnetic field exerts a force on an electron, it causes it to accelerate and change direction.

If the mass \( m \) of the electrons increases, their acceleration \( a \), given the same force \( F \), will decrease. This results in a smaller deflection of the electron beam. In essence, larger mass particles are less easily deflected than lighter ones under the same force.

• Predicts the impact of mass changes on electron deflection.
• Explains the inverse relationship between acceleration and mass.

Understanding Newton's Second Law is critical for predicting how altering particle characteristics affects their trajectory in magnetic fields.

Particle Deflection

Particle deflection in a cathode-ray tube involves the deviation of a beam’s path due to interactions with magnetic or electric fields. This concept is central to the functionality of devices like CRTs, used to display images.

Several factors influence how particles are deflected in a magnetic field, including particle charge, velocity, magnetic field strength, and mass. Each aspect modifies how much and in what way electrons deviate from their initial path.

• Charge: A higher charge increases the force and thus the deflection.
• Velocity: Higher velocity can increase deflection by increasing the Lorentz force but may also decrease interaction time.
• Magnetic Field: Stronger fields result in greater force and deflection.
• Mass: Heavier particles experience less deflection due to reduced acceleration.

Through managing these variables, CRTs control the position of electron beams, influencing the accuracy and resolution of the displayed image. Particle deflection, therefore, is not just a theoretical concept but a practical tool in visual technology.