As a soccer ball arcs through the air from one end of the field to the other, its path follows the characteristic pattern of a projectile, a parabolic trajectory.  In the previous lab activity you used a computer simulation to discover that a charged particle can also move through a parabolic trajectory.  The analysis of the data from the simulation revealed that the same equations that you used to analyze projectile motion in previous courses can be applied to a charged particle moving through a uniform electric field.

Image by Phillip Kofler from Pixabay

 

Self-Check

Answer the following self-check (SC) question then click the "Check your work" bar to assess your response.


SC 19.  

The following diagram shows an electron entering the region between two oppositely charged plates.  The plates are 55.0-mm long and are separated by 19.5 mm.  A potential difference of 0.133 V across the plates generates a uniform electric field in the region between the plates.  The electron is given an initial velocity of 8.50 × 10 5 m/s in the positive y direction.  Use this information to determine the final velocity of the electron when it leaves the region between the plates.

 

Be sure to begin your solution with a free-body diagram and an analysis of the physics principles that will support your solution.

 

 


Self-Check Answer

SC 19.

Given

 

Required

The magnitude and direction of the final velocity of the electron.

 

Analysis and Solution

Step 1: Free-body diagram and statement of the physics principles.

 

  • The electric field between the plates points in the negative  x  direction.

  • Since the particle is negatively charged, the electrostatic force on the particle will act in the positive  x  direction.

  • The electrostatic force will cause the particle to accelerate in the positive  x  direction. This is in accordance with Newton's second law of motion.

  • Since there is no unbalanced force acting in the  y  direction, the particle will move with uniform motion in the positive  y  direction. This is in accordance with Newton's first law of motion.

  • The path of the particle is a parabolic trajectory. This is a consequence of uniform motion in the positive  y  direction combined with accelerated motion in the positive  x  direction.

Step 2: Determine the magnitude of the electrostatic force.

 

 

Step 3: Determine the magnitude of the acceleration in the positive  x  direction

 

 

Step 4: Determine the time for the particle to travel to the end of the region between the plates. Use the fact that the motion in the  y  direction is uniform.

 

 

Step 5: Determine the final velocity in the  x  direction.

 

 

Step 6: Use the  x  and  y  components to find the final velocity. Since the motion in the  y  direction is uniform  v f y  = +8.50 × 10 5  m/s.

 

 

 


 

Paraphrase

The final velocity of the electron when it leaves the region between the plates is 8.54 × 10 5  m/s [85°].