Question

A charged particle moves between two electrically charged plates, as shown here.\(\begin{array}{l}{\text { (a) What is the sign of the electrical charge on the particle? }} \\ {\text { (b) As the charge on the plates is increased, would you ex- }} \\ {\text { pect the bending to increase, decrease, or stay the same? }}\end{array}$$\begin{array}{l}{\text { (c) As the mass of the particle is increased while the speed of }} \\ {\text { the particles remains the same, would you expect the bending }} \\ {\text { to increase, decrease, or stay the same? [Section } 2.2 ]}\end{array}\)

Short answer

In short, (a) the sign of the electrical charge on the particle can be determined by observing the direction of the bending in the particle's path. (b) As the charge on the plates is increased, the bending of the particle's path is expected to increase due to a stronger electric field and force experienced by the particle. (c) If the mass of the particle is increased while keeping its speed constant, the bending of the particle's path is expected to decrease as the acceleration will be reduced.

Step-by-step solution

Part (a): Sign of the electrical charge on the particle

To determine the sign of the electrical charge on the particle, we must consider how the electrical forces on the particle are interacting with the charged plates. As the particle moves between the plates, it must experience a force that is deflecting it due to the electrical interaction between the particle and the electric field generated by the plates. Suppose the top plate has a positive charge and the bottom plate has a negative charge. If the particle is positively charged, it would be repelled by the top plate and attracted by the bottom plate, causing it to bend downward. Conversely, if the particle is negatively charged, it would be attracted by the top plate and repelled by the bottom plate, causing it to bend upward. By observing the direction of the bending in the particle's path, we can determine the sign of the electrical charge on the particle.

Part (b): The effect of increasing the charge on the plates on bending

When the charge on the plates is increased, the electric field between them will also increase. Due to this increased electric field, the force experienced by the moving particle will be greater. As the force on the particle increases, the acceleration of the particle in the direction of the force will increase as well, causing the particle to bend more. Based on this information, we can expect that the bending will increase as the charge on the plates is increased.

Part (c): The effect of increasing the mass of the particle on bending

To analyze the effect of increasing the mass of the particle while keeping its speed constant, we must consider the equation for acceleration: \(a = F/m\) where a is the acceleration, F is the force experienced by the particle, and m is the mass of the particle. Since the speed of the particle remains constant, the force that the particle experiences from the electric field between the plates will also remain constant. Thus, if the mass of the particle were to increase, the acceleration of the particle would decrease, according to the equation above. A decrease in acceleration means that the particle will need more distance to change its path, so we can expect the bending to decrease as the mass of the particle is increased while keeping the speed constant.

Key concepts

Charged Particles

Charged particles are fundamental components in the study of electric fields. They possess either a positive or a negative electric charge. This charge is responsible for how particles interact with each other and with electric fields.

In situations involving charged plates, such as parallel plate capacitors, charged particles exhibit unique behaviors based on their charge sign. For instance:

• A positively charged particle would be attracted to a negatively charged plate and repelled by a positively charged plate.
• Conversely, a negatively charged particle would be attracted to a positively charged plate and repelled by a negatively charged plate.

Understanding these interactions helps in determining not only the motion of the particle but also the direction of the electric force acting upon it. This concept is crucial when analyzing how a particle bends or accelerates due to electric influences.

Electric Force

The electric force is a powerful force responsible for the interactions between charged particles and fields. It operates based on the fundamental principle that opposite charges attract and like charges repel. This force depends on the magnitude of the charges involved and the distance between them, as described by Coulomb's law.

When a charged particle moves through an electric field created by charged plates, it experiences electric force which causes it to accelerate or change direction. The direction of the force is determined by:

• The sign of the charge on the particle.
• The polarity of the plates.

The force's strength can be altered by changing the charge on the plates. An increased charge results in a stronger force, affecting the particle's trajectory more intensely by causing greater bending.

Acceleration

Acceleration is the rate at which an object's velocity changes with time. In the context of electric fields, charged particles undergo acceleration due to forces from electric fields. This acceleration is determined by Newton's second law of motion, which states:

\[a = \frac{F}{m}\]

Where:

• \( a \) is the acceleration,
• \( F \) is the force applied (in this case, the electric force),
• \( m \) is the mass of the particle.

Increasing the electric force leads to increased acceleration, assuming mass remains constant. However, if the mass of the particle increases while the force stays constant, the acceleration decreases. This principle explains why heavier particles experience less bending along their paths in an electric field environment.

Electric Field Influence

Electric fields are invisible fields that exert forces on charged particles. The influence of an electric field on a charged particle dictates how the particle moves. Whether the particle accelerates or bends depends heavily on the strength and direction of the electric field.

Several factors influence an electric field's effect on charged particles:

• Strength of the electric field: Greater field strength results in a stronger force on the particles.
• Orientation of the electric field: Dictates the direction of the force experienced by the charged particles.

When particles move through these fields, they are propelled in the direction of the force. Thus, increasing the charge on the plates will further strengthen the electric field, causing more pronounced bending or movement, demonstrating the field's significant influence on particle behavior.