Motion of a Charged Particle in an Electric Field

In summary, we have a proton moving at 4.50 x 108 m/s in the horizontal direction and entering a uniform vertical electric field with a magnitude of 9.60 x 103 N/C. Using the equation \vec{a} = q\vec{E} / m, we can find the time interval required for the proton to move 5.00 cm horizontally, which is equal to its velocity divided by 5.00 cm. Its vertical displacement during that time interval is 5.68 mm. The horizontal component of its velocity remains constant, while the vertical component can be found by using the time interval and acceleration calculated in part (b). Therefore, the horizontal and vertical components of its velocity after traveling
  • #1
zandbera
18
0

Homework Statement


A proton moves at 4.50 x 108 m/s in the horizontal direction. It enters a uniform vertical electric field with a magnitude of 9.60 x 103 N/C. Ignoring any gravitational effects, find (a) the time interval required for the proton to move 5.00 cm horizontally, (b) its vertical displacement during that time interval, and (c) the horizontal and vertical components of its velocity after it has traveled 5.00 cm horizontally.


Homework Equations


[tex]\vec{a}[/tex] = q[tex]\vec{E}[/tex] / m


The Attempt at a Solution


(a) Since it's moving at constant horizontal velocity, and the only force its encountering is a vertical force, would the particle continue to move at the constant horizontal speed? Which would mean that the time interval to move 5.00 cm is just its velocity / 5.00 cm??

(b) I don't know how to relate the electric field to the velocity. But I know that the initial vertical velocity is 0, right?

(c) If i was right in (a) then its horizontal component will be the same
 
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  • #2
zandbera said:
(a) Since it's moving at constant horizontal velocity, and the only force its encountering is a vertical force, would the particle continue to move at the constant horizontal speed?
Right.
Which would mean that the time interval to move 5.00 cm is just its velocity / 5.00 cm??
You have that fraction upside down. Distance = velocity*time.

(b) I don't know how to relate the electric field to the velocity.
But you know how to find the acceleration caused by the electric field. The rest is kinematics.
But I know that the initial vertical velocity is 0, right?
Right.

(c) If i was right in (a) then its horizontal component will be the same
That's true.
 
  • #3
(b) From the equation and my given data, is qE = 9.60 x 10^3 N/C or is it just E = 9.60 x 10^3?

If it's E = 9.60 x 10^3, I would just multiply by (+e) to get qE and then divide by the mass of a proton, right?
 
  • #4
Okay yeah for (b) I did what I thought, I used E = 9.60 x 10^3, then multiplied by +e, divided by mass of proton to get a, then used delta x = Vi t + 1/2 a t^2 with Vi = 0, and i got 5.68 mm, the correct answer.

So then for (c), the horizontal component is just the initial horizontal velocity, and then i can use the time interval from (a) and the acceleration from (b) to find the vertical velocity, so would those be my two components?
 
  • #5
zandbera said:
So then for (c), the horizontal component is just the initial horizontal velocity, and then i can use the time interval from (a) and the acceleration from (b) to find the vertical velocity, so would those be my two components?
Right!
 

1. What is the motion of a charged particle in an electric field?

The motion of a charged particle in an electric field refers to the movement of the particle when it is placed in an area where there is an electric field. The electric field exerts a force on the particle, causing it to move in a particular direction.

2. How does the direction of the electric field affect the motion of a charged particle?

The direction of the electric field has a significant impact on the motion of a charged particle. If the electric field is in the same direction as the particle's velocity, the particle will experience an increase in speed. However, if the electric field is in the opposite direction, the particle will decelerate and eventually come to a stop.

3. What is the equation for calculating the force on a charged particle in an electric field?

The equation for calculating the force on a charged particle in an electric field is F = qE, where F is the force, q is the charge of the particle, and E is the strength of the electric field. This force is always perpendicular to the direction of the electric field.

4. Can a charged particle's motion in an electric field be predicted?

Yes, a charged particle's motion in an electric field can be predicted. By using the equations for force and acceleration, along with the particle's initial conditions such as velocity and position, the particle's future motion can be calculated.

5. How does the mass of a charged particle affect its motion in an electric field?

The mass of a charged particle does not affect its motion in an electric field. The force and acceleration of the particle are directly proportional to the particle's charge, and mass does not play a role in these calculations. Therefore, a particle with a larger mass will experience the same motion as a particle with a smaller mass in the same electric field.

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