How Do You Calculate the Electric Field of a Dipole at a Specific Point?

AI Thread Summary
To calculate the electric field of a dipole at a specific point, the formula used is E = 2qs/(4πE * r^3), where E is the permittivity of vacuum. Given the dipole with charges of +4 nC and -4 nC separated by 2 mm, and evaluated at a point 5 cm away, the initial calculation yielded 2.88 N/C. The user identified an error in their computation, specifically neglecting to cube the distance d in the formula. Additionally, it was noted that the electric field perpendicular to the dipole is half of that on the axis, suggesting a value of 1.44 N/C for the perpendicular field. The discussion highlights the importance of careful unit conversion and adherence to the formula's requirements.
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Homework Statement


A dipole consists of two charges +q and -q, held apart by a rod of length s, as shown in the diagram. If q = 4 nC and s = 2 mm, what is the magnitude of the electric field due to the dipole at location A, a distance d = 5 cm from the dipole?

The diagram shows point A being on axis with the dipole.

Homework Equations



The formula for on axis is 2qs/4piE*r^3, where E is the permittivity of vacuum

The Attempt at a Solution



So to solve this first I converted all units

q = 4nC = 4e-9C
s = 2mm = .002m
d = 5cm = .05m

Then I plug in the values into the formula

2*4e-9C*.002m/4pi*8.85e-12*.05m = 2.88N/C
But that seems to be the wrong answer can someone please tell me what I'm doing wrong
and also is it true that the field perpendicular to the dipole is just half of what it would be if it was on axis. If that's true than the field 5cm perpendicular to the dipole should be just half of what I come up with, in this case 1.44N/C.

Thank You for your help
 
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Oh I think I figured out where I went wrong I forgot to cube d,
 
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