Electric Potential related to velocity

In summary, the charged particle will have 7 m/s of kinetic energy when it reaches the 200V potential difference.
  • #1
jeandempsey
6
0

Homework Statement


A +3μC charge with a mass of 2 x 10 ^-4 kg is moving with a speed of 5 m/s at a position where the electric potential is 1000 V. How fast will it be moving when it gets to a position where the electric potential is 200 V? Assume energy is conserved.


Homework Equations


V=electric potential energy / q
D=Vot+1/2at2
KE=1/2mv^2

The Attempt at a Solution


I got the change in electric potential energy to be .0024. And then I set that equal to the kinetic energy equation. I got my answer to be 24m/s, but the answer is 7 m/s. I think I might be doing this totally wrong.
 
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  • #2
jeandempsey said:

Homework Statement


A +3μC charge with a mass of 2 x 10 ^-4 kg is moving with a speed of 5 m/s at a position where the electric potential is 1000 V. How fast will it be moving when it gets to a position where the electric potential is 200 V? Assume energy is conserved.


Homework Equations


V=electric potential energy / q
D=Vot+1/2at2
KE=1/2mv^2

The Attempt at a Solution


I got the change in electric potential energy to be .0024. And then I set that equal to the kinetic energy equation. I got my answer to be 24m/s, but the answer is 7 m/s. I think I might be doing this totally wrong.

In what way did you "set that equal to the kinetic energy equation"? Did you account for the kinetic energy due to the initial velocity? Perhaps you should show the calculation that you performed.
 
  • #3
I did this: my electric potential energy was -2.4x10^-3
So- -2.4x10^-3 = 1/2(2x10^-4)v^2
 
  • #4
jeandempsey said:
I did this: my electric potential energy was -2.4x10^-3
So- -2.4x10^-3 = 1/2(2x10^-4)v^2

There was an initial velocity, so an initial kinetic energy. The change in potential results in a change in the kinetic energy, not the total.
 
  • #5
Thank you, but I'm still kind of confused as to how you would get the velocity from that
 
  • #6
jeandempsey said:
Thank you, but I'm still kind of confused as to how you would get the velocity from that

What is the relationship between kinetic energy and speed? What, then, is the initial kinetic energy of the charged particle to begin with? Then, when it has moved across the 1000V to
200V potential difference its kinetic energy will have CHANGED from that initial value.

If you want to look at the situation as a single formula, then using the law of conservation of energy you can write that the sum of the kinetic energy and potential energy for the system is constant. So that

[itex] KE_1 + PE_1 = KE_2 + PE_2 [/itex]
 

1. What is electric potential and how is it related to velocity?

Electric potential is the potential energy per unit charge at a specific point in an electric field. It is related to velocity through the equation V = Ed, where V is the electric potential, E is the electric field strength, and d is the distance traveled. This equation shows that as velocity increases, the electric potential also increases.

2. Why is electric potential related to velocity important in science?

Understanding the relationship between electric potential and velocity is important in many fields of science, including physics, chemistry, and engineering. It helps us understand how electric fields and charges interact with each other, and is crucial in designing and optimizing electrical systems and devices.

3. How does electric potential related to velocity affect the movement of charged particles?

The electric potential acts as a force on charged particles, causing them to accelerate in the direction of the electric field. As velocity increases, the electric potential also increases, resulting in a greater force and acceleration on the charged particles.

4. Can electric potential related to velocity be negative?

Yes, electric potential can be negative. This occurs when the direction of the electric field is opposite to the direction of the particle's motion. In this case, the particle's kinetic energy decreases, resulting in a negative change in electric potential.

5. How can electric potential related to velocity be measured experimentally?

Electric potential can be measured experimentally using a voltmeter, which measures the potential difference between two points in an electric field. To measure the potential related to velocity, the voltmeter can be connected to a moving charged particle, and the change in electric potential can be measured as the particle moves through the electric field.

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