Calculating Electric Field due to a Dipole

[guitarman]

Homework Statement

Two dipoles are oriented as shown in the diagram below. Each dipole consists of two charges +q and -q, held apart by a rod of length s, and the center of each dipole is a distance d from location A. If q = 4 nC, s = 1 mm, and d = 6 cm, what is the electric field at location A?

As I am unaware of how to attach a file, here is a diagram
************+
************-
************|
************|
************|
************|
-***********|
+--------------A

the *s are there for formatting, or the else lines do not align

Homework Equations

(1/4*pi*epsilon)*(2qs/d^3) is the electric field of a dipole, on the dipole axis
and
(1/4*pi*epsilon)*(qs/d^3) is the electric field of a dipole, perpendicular to the dipole axis

The Attempt at a Solution

Plugging the values given, I used the latter equation for the x component, and by doing (9e9)(4e-9*1e-3)/(6e-2)^3 I obtained 166 N/C.

I used the first equation for the y component and obtained 333 N/C

I know there is no z component, so I input <166, 333, 0> N/C, yet this is wrong. Can somebody explain to me what I am doing? I attempted submitting -166 for the x component in case I had somehow misinterpreted the direction of the field, but that was also wrong. Does anybody understand what I am doing wrong?

 

[rl.bhat]

In the dipole above A, the negative charge is closer to A . So the attractive force is more than the repulsive force. So the electric field is towards the dipole.
In the equatorial position the direction of the field is parallel to the dipole from positive charge to negative charge.
Hence the electric field due to two dipoles are in the same direction. So the net field is the sum of them.

 

[tomcue]

Hello,

Thank you for sharing your work and question. Your approach to solving this problem is correct, however, there is a mistake in the values you have used for the length of the dipole (s) and the distance from the dipole to location A (d).

In the problem statement, it is given that s = 1 mm and d = 6 cm. However, in your calculation, you have used s = 1 m (1 millimeter) and d = 6 m (6 meters). This is why your calculated values for the electric field components are incorrect.

To correct this, you can either convert the given values to meters before plugging them into the equations, or you can use the values given in the problem statement and convert the final answer to N/C.

I hope this helps clarify your confusion. Keep up the good work!