Electric Field due to a Dipole (not on a z-axis)

In summary: They don't cancel.In summary, the electric field at point P due to the electric dipole is very small and can be approximated to be zero. However, using the angle theta, the magnitude of the electric field can be represented as E_y = (2q/R)sin(theta). The rest of the solution involves finding R and sin(theta) in terms of r and d and calculating the final result.
  • #1
Oijl
113
0

Homework Statement


The figure shows an electric dipole. What is the magnitude of the dipole's electric field at point P, located at distance r >> d?

hrw7_22-38.gif



Homework Equations




The Attempt at a Solution



I suppose I could define the angle with which I could write Ey = Esin[tex]\theta[/tex], but this problem is a webassign.com problem, so it's online and I can't define anything.

The magnitude of the electric field at p due to the dipole would be very small, and I first estimated it to be zero (since the problem asks for an estimation anyway).

Without defining and using a theta, how could I represent the magnitude of the electric field?
 
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  • #2
Just introduce theta temporarily. It goes away in the end since you know what it is.

The electric field vectors of the two charges add in the [itex]y[/itex] direction and cancel in the [itex]x[/itex] direction. Hence
[tex]
|\vec E| = |E_y| = (2 q/R) \sin(\theta)
[/tex]
where I will let you write down [itex]R[/itex] and [itex]\sin(\theta)[/itex] in terms of [itex]r[/itex] and [itex]d[/itex].

The rest you can do.
 
  • #3
loveequation said:
Just introduce theta temporarily. It goes away in the end since you know what it is.

The electric field vectors of the two charges add in the [itex]y[/itex] direction and cancel in the [itex]x[/itex] direction. Hence
[tex]
|\vec E| = |E_y| = (2 q/R) \sin(\theta)
[/tex]
where I will let you write down [itex]R[/itex] and [itex]\sin(\theta)[/itex] in terms of [itex]r[/itex] and [itex]d[/itex].

The rest you can do.
In the dipole one is +ve charge and the other -ve charge.
The electric field E = 1/4πεο*q/[r2 + (d/2)2]
Their y-components cancel out and x-components add.
 
  • #4
I maintain that the y components add. Think of the magnetic field lines of the Earth at the equator.
 

1. What is an electric dipole?

An electric dipole is a pair of equal and opposite electric charges that are separated by a small distance. It can also refer to any object that has two poles with opposite electric charges, similar to a magnet.

2. How is the electric field calculated for a dipole?

The electric field due to a dipole is calculated by adding the individual electric fields from each charge. The magnitude of the electric field at a point is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them.

3. Can the electric field due to a dipole be zero?

Yes, the electric field due to a dipole can be zero at a specific point between the two charges. This occurs when the distance between the two charges is equal to the distance from the point to the charges and the charges have equal magnitude but opposite signs.

4. How does the orientation of a dipole affect the electric field?

The orientation of a dipole affects the direction of the electric field. If the dipole is aligned with the electric field, the field lines will be parallel to the dipole axis. If the dipole is perpendicular to the electric field, the field lines will be directed from the positive to the negative charge.

5. What are some real-life examples of electric dipoles?

Some common examples of electric dipoles include water molecules, which consist of a positive and negative charge due to the uneven distribution of electrons, and radio antennas, which have positive and negative charges at opposite ends to create an oscillating electric field.

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