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}\)

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.

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.

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.