Electric potential problem. Conceptual.

In summary, an electron moving parallel to the x-axis with an initial speed of V1 at the origin is reduced to a speed of V2 at x=2. The potential difference between the origin and x=2 is calculated, and it is determined that the origin is at a lower potential despite initial reasoning that x=2 would be at a higher potential due to deceleration along the positive x-axis in the presence of an electric field.
  • #1
haydn
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Problem: An electron moving parallel to the x-axis has an initial speed of V1 at the origin. It's speed is reduced to V2 at the point x=2 (V2<V1). Calculate the potential difference between the origin and the point x=2. Which point is at the higher potential?

I was able to calculate the potential difference pretty easily but I got the second part wrong. I thought the higher potential would be at the point x=2 but the book says the origin. Here is my reasoning, please tell me where I'm going wrong:

Since the electron is decelerating along the positive x-axis, it is experiencing a force due to an electric field pointing in the -x direction. Since electric potential decreases as you move along the direction of an electric field, the origin should be at lower potential.

Thanks.
 
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  • #2
Hi haydn! :smile:
haydn said:
Since the electron is decelerating along the positive x-axis, it is experiencing a force due to an electric field pointing in the -x direction. Since electric potential decreases as you move along the direction of an electric field, the origin should be at lower potential.

hmm :rolleyes: … would this be one of those negatively charged electrons? :wink:
 
  • #3


Your reasoning is correct up to a certain point. The mistake you are making is assuming that the electron is experiencing a uniform electric field in the -x direction. In reality, the electric field is not constant but rather decreases as the electron moves along the x-axis. This is because the electric field is created by a charged particle, which has a stronger field closer to it and a weaker field farther away.

Since the electric field is decreasing along the x-axis, the potential difference between two points will also decrease as you move along the direction of the electric field. Therefore, the point with the higher potential will be the one with the lower electric field, which in this case is the origin.

To understand this concept better, think of it as a hill. The top of the hill has a higher potential because it is at a higher point, but as you move down the hill, the potential decreases. Similarly, the origin has a higher potential because it is at a higher point in the electric field, but as you move along the x-axis, the potential decreases.

I hope this helps clarify the concept for you. Keep up the good work in your studies!
 

1. What is electric potential?

Electric potential is a measure of the amount of electric potential energy per unit charge at a given point in an electric field. It is similar to the concept of height in a gravitational field, and it is measured in volts (V).

2. How is electric potential different from electric field?

Electric field is a vector quantity that describes the force per unit charge at a given point in an electric field. Electric potential, on the other hand, is a scalar quantity that describes the potential energy per unit charge at a given point. In other words, electric field tells us about the force acting on a charge, while electric potential tells us about the energy of that charge.

3. What is the relationship between electric potential and electric field?

Electric potential and electric field are related by the equation E = -∇V, where E is the electric field, V is the electric potential, and ∇ is the gradient operator. This means that the electric field is the negative gradient of the electric potential.

4. How is electric potential used in practical applications?

Electric potential is used in many practical applications, such as in the design of electrical circuits, power generation and distribution, and electronic devices. It is also used in medical technology, such as in electrocardiography (ECG) to measure the electrical activity of the heart.

5. What factors affect the electric potential at a given point?

The electric potential at a given point is affected by the amount and distribution of charge, the distance from the source of the electric field, and the medium through which the electric field is passing. It is also affected by the presence of other charges and conductors in the vicinity.

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