# Expression for Magnitude of Electric Field by dipole integral

1. Jun 30, 2016

### elements

1. The problem statement, all variables and given/known data
Consider the electric dipole seen in the notes. (a) Using integration, derive an expression for the magnitude of the electric field produced by the dipole at any point along the x-axis.

Electric Dipole: http://labman.phys.utk.edu/phys136/modules/m5/images/electr5.gif

2. Relevant equations
Electric Field Equation, Differential Form $${d \vec E} =\frac 1 {4\pi\epsilon_0} \frac {dq} {r^2} \hat {\mathbf r}$$
Linear Charge Density $$dq = \lambda dx$$
electric dipole: $$\vec p = q\vec d$$

3. The attempt at a solution
I am completely confused as to how to get started or which equation to integrate to obtain the equation. I am aware that the y-components of the point charges cancel each other out, hence only the charge along the x-axis matters. As well as the general integration needed to be done to obtain the formula.$$\int_{-\infty}^{\infty} F$$ where F is the function to integrate.

Last edited: Jun 30, 2016
2. Jun 30, 2016

### blue_leaf77

The picture you posted doesn't seem to correspond to the problem you are trying to solve. That picture is more inclined for a problem about electric dipole motion under external electric field and has nothing to do with a charged rod. Moreover, where is the mentioned x axis in that picture?

3. Jul 1, 2016

### elements

I believe the problem would be attuning to the effects of two point charges creating a dipole along the x-axis, in the picture it would be the E line. Im trying to figure out how to properly set the problem up for integration as I can't seem to figure out how to relate dE and p, so it can be proven with integration all I've been able to find is the derivation using binomial expansion theorems

4. Jul 1, 2016

### blue_leaf77

I don't see why there should be integration involved. According to that picture, the only parts of the dipole which is charged are its tips. The connecting rod itself is neutral.

5. Jul 1, 2016

### elements

Then would there be a scenario for the derivation of the magnitude of the electric field that would require integration?