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# Figure 1.30 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Last updated date: 15th Jun 2024
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Hint: In a uniform electrostatic field, positively charged particles will be accelerated in the direction of the field, and negatively charged particles will be accelerated in the opposite direction. The deflection or curvature of a particle's trajectory in an electric field depends on its charge-to-mass ratio; a greater charge-to-mass ratio will result in a more pronounced curvature.

Step by Step Solution:

Step 1: Determine the direction of the electrostatic field.

The uniform electrostatic field is indicated by the parallel lines with "+" symbols. The field direction is from positive to negative, which means it's from top to bottom in this image.

Step 2: Analyze the trajectories of the three particles.

Particle 1 is deflecting upwards, away from the field direction.

Particle 2 is moving straight without any deflection.

Particle 3 is deflecting downwards, in the direction of the field.

Step 3: Determine the charge of each particle.

Particle 1 is moving opposite to the field direction, so it must be negatively charged.

Particle 2 is not deflected by the field, which means it is neutral (no charge).

Particle 3 is moving in the direction of the field, so it must be positively charged.

Step 4: Determine the charge-to-mass ratio.

The curvature of the trajectory is influenced by the charge-to-mass ratio. A particle with a higher charge-to-mass ratio will have a more pronounced deflection in the field.

Particle 1 has a pronounced curvature upwards.

Particle 3 has a slight curvature downwards.

Comparing the two, Particle 1 has a more pronounced deflection, indicating a higher charge-to-mass ratio compared to Particle 3.

Note: It's important to understand that the amount of deflection or curvature of a charged particle's path in an electrostatic field depends on both its charge and its mass. A particle with a larger charge or a smaller mass will have a larger charge-to-mass ratio and, consequently, will experience a more pronounced deflection in its trajectory when subjected to the field. In this problem, the curvature of Particle 1's trajectory indicates that it has the highest charge-to-mass ratio among the three particles.