Electric Potential From Electric Field

In summary, the conversation discusses two particles with charges q1 and q2 separated by a distance d. The net electric field due to the particles is zero at a point on the x-axis located at x=d/4. The conversation also mentions finding a point on the x-axis (other than infinity) at which the electric potential due to the two particles is zero, with V=0 at infinity. It is suggested that this point may be located in the middle of the two charges if they are equidistant from the origin.
  • #1
doubedylan
3
0

Homework Statement


Two particles, of charges q1 and q2 are separated by distance d. The net electric field due to the particles is zero @ x=d/4.
With V=0 @ infinity, locate (in terms of d) any point on the x axis (other than infinity) at which the electric potential due to the two particles is zero.


Homework Equations


V=-[tex]\int[/tex][tex]^{f}_{i}[/tex] ([tex]\vec{E}[/tex] [tex]\bullet[/tex] d[tex]\vec{s}[/tex])


The Attempt at a Solution


Seems too obvious to be true, but I think V = 0 @ d/4 since E=0 as well.
Anyone see where else is could be?
 
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  • #2
Pretend like the two particles are equidistant from the origin, therefore the origin is the middle of the two charges. When finding potential at a point, it is the potential of one charge on the point plus the potential of the other charge on the point. Potential is not a vector, so I believe if the charges are the same, you will find your answer in the middle of the two charges.
 
  • #3


I would like to provide a more thorough response to this question. First, let's define some terms and concepts to better understand the problem at hand.

Electric potential is a measure of the potential energy per unit charge at a given point in an electric field. It is a scalar quantity and is measured in volts (V).

Electric field, on the other hand, is a vector quantity that describes the strength and direction of the electric force on a charged particle. It is measured in newtons per coulomb (N/C).

In order to determine the electric potential at a point, we can use the formula V = -∫E•ds, where E is the electric field and ds is the infinitesimal displacement along the path of integration.

In this problem, we are given that the net electric field due to the two particles is zero at x = d/4. This means that the electric forces from the two particles cancel out at this point, resulting in a net electric field of zero.

Since the electric field is zero at x = d/4, we can conclude that the electric potential at this point is also zero. This is because the integral of a zero vector is always zero, meaning that the potential difference between any two points along this path is also zero.

Now, the question asks us to find another point on the x-axis (other than infinity) where the electric potential is also zero. Since we know that the electric potential is zero at x = d/4, we can use this point as one of the limits of integration in our formula for electric potential.

Let's choose the other limit of integration to be x = x0, where x0 is the point we are trying to find. This means that we want to solve for x0 such that the electric potential is zero between x = d/4 and x = x0.

Using the formula V = -∫E•ds, we can set up the following integral:

0 = -∫E•ds = -∫x0 d/4 E•ds

Since we know that the electric field is zero at x = d/4, we can simplify this integral to:

0 = -∫x0 d/4 0•ds = 0

This shows that the electric potential is indeed zero at x = x0, and thus we have found another point (x0) on the x
 

1. What is electric potential?

Electric potential is the amount of electrical potential energy that a charged particle possesses per unit charge. It is similar to gravitational potential energy, but with electric charges instead of masses.

2. How is electric potential related to electric field?

The electric potential is directly related to the electric field. The electric field is a measure of the force that a charged particle experiences at a given point, while the electric potential is a measure of the potential energy that a charged particle has at that point. In other words, the electric field is the gradient of the electric potential.

3. Can the electric potential be negative?

Yes, the electric potential can be negative. This indicates that the electric field is directed towards the source of the negative potential. In other words, a negative potential means that a charged particle will move from a higher potential to a lower potential.

4. How is electric potential calculated from electric field?

The electric potential can be calculated using the equation V = -∫E∙dr, where V is the electric potential, E is the electric field, and dr is the displacement vector. This equation takes into account the work done by the electric field on a charged particle as it moves from one point to another.

5. What is the unit of electric potential?

The SI unit of electric potential is volts (V). It is also commonly expressed in joules per coulomb (J/C) or newtons per coulomb (N/C). These units represent the amount of energy per unit charge at a given point in an electric field.

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