Finding the electric field of a electric quadrupole

In summary, the conversation discusses one type of electric quadrupole and how to determine the electric field at points along the perpendicular bisector. The equation for the electric field is E=(1/4\pi\epsilon0)*(p/r3) and the value of p is determined to be Ql. The conversation also mentions using the Taylor Series and adding the electric fields at different points to get the total electric field.
  • #1
n387g
8
0
One type of electric quadrupole consists of two dipoles places end to end with their negative charges (say) overlapping; that is, in the center is -2Q flanked (on a line) by a +Q to either side. Determine to electric field, E, at points along the perpendicular bisector and show that E decreases as 1/r4. Measure r from the -2Q charge and assume r>>l.


E+=E-=(1/4[tex]\pi[/tex][tex]\epsilon[/tex]0)*(Q/(r2+(l2/4)
p=Ql



The Attempt at a Solution


First I broke the electric fields into the x and y axes.
Where, Ex=0
For the Ey, I used the equation E=(1/4[tex]\pi[/tex][tex]\epsilon[/tex]0)*(p/r3)
Then, substituted p for (Q*l) and then r3 for r4
I assume there must be more to it than that, but I'm at a loss.
 

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  • #2
E+ is not = E-
 
  • #3
Okay, so you have to add the electric fields at the +Q, -2Q and +Q.
So for +Q, E=k(Ql/(l2+r2)^(1/2)) (cos(theta)rx+sin(theta)ry)
And the for -2Q, E=k(2Ql/r2)(sin(theta)ry)
And for the other +Q, E=k(Ql/(l2+r2)^(1/2)) (-cos(theta)rx+sin(theta)ry)
Is this the correct way to do this?
 
  • #4
n387g said:
+Q, E=k(Ql/(l2+r2)^(1/2)) (cos(theta)rx+sin(theta)ry)

Whats that l after Q
 
  • #5
it's a lowercase L, for length
 
  • #6
Using the equation where p=Ql
 
  • #7
Do you know about Taylor Series ?
 

1. What is an electric quadrupole?

An electric quadrupole is a system of two positive and two negative charges arranged in a specific configuration. It is characterized by its quadrupole moment, which describes the distribution of the charges within the system.

2. Why is it important to find the electric field of an electric quadrupole?

Understanding the electric field of an electric quadrupole is important in various fields of science, such as electrostatics, electromagnetism, and quantum mechanics. It helps in analyzing the behavior of electric charges and the influence of external electric fields on the system.

3. How do you calculate the electric field of an electric quadrupole?

The electric field of an electric quadrupole can be calculated using the formula E = (1/4πε0) * (3(cosθ/r3) - (1/r3)), where ε0 is the permittivity of free space, θ is the angle between the point where the field is being measured and the axis of the quadrupole, and r is the distance between the point and the axis.

4. What is the difference between an electric dipole and an electric quadrupole?

An electric dipole has two opposite charges separated by a small distance, while an electric quadrupole has two positive and two negative charges arranged in a specific configuration. The electric field of a dipole decreases inversely with the cube of the distance, while the electric field of a quadrupole decreases inversely with the fourth power of the distance.

5. Can the electric field of an electric quadrupole be zero?

Yes, the electric field of an electric quadrupole can be zero at certain points, known as equipotential points. These points are located along the axis of the quadrupole and are equidistant from the four charges. At these points, the electric field vectors from the positive and negative charges cancel out, resulting in a net electric field of zero.

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