Force of Dipole on Proton: Calculating E and F

[elli]

Homework Statement

A dipole is centered at the origin, and is composed of charged particles with charge +e and -e, separated by a distance 7 ✕ 10-10 m along the y axis. The +e charge is on the -y axis, and the -e charge is on the +y axis. A proton is located at <0, 3 ✕ 10-8, 0> m. What is the force on the proton, due to the dipole?

Homework Equations

E=k*[(2*q*s)/(r^3)]
F=E*q

The Attempt at a Solution

I calculated the electric field using the equation for a charged particle on axis with a dipole. I then multiplied that electric field by the charge of the proton(1.6e-19)
I'm very lost with all this dipole stuff. Any and all help is appreciated!

 

[gneill]

Show the equation that you used. Sketch the relative positions of the particles. Hint: you'll only need one axis to do it!

 

[elli]

What I have is k=9e9
q=-1.6e-19
s=7e-10
r=(3e-8)-(7e-10/2)=2.965e-8
E=-77342.2N/C
The charge of the proton is 1.6e-19
I think the force should therefore be (0,1.6e-19*-77342.2,0)=(0,-1.237e-14,0).
But that's just not working:(

 

[gneill]

What coordinate axis are the dipole electrons on?

What coordinate axis is the proton on?

 

[Nickie]

Firstly, the electric field at a point due to a dipole can be calculated using the formula E = k * (2 * q * s) / r^3, where k is the Coulomb's constant, q is the magnitude of the charges on the dipole, s is the separation between the charges, and r is the distance from the dipole to the point where the electric field is being calculated. In this case, r can be calculated as the distance between the dipole and the proton, which is 3 * 10^-8 m.

Using the given information, we can calculate the electric field at the proton's location by substituting the values into the formula: E = (9 * 10^9) * [(2 * 1.6 * 10^-19 * 7 * 10^-10) / (3 * 10^-8)^3] = 1.792 N/C.

Now, to calculate the force on the proton, we can use the formula F = E * q, where F is the force, E is the electric field, and q is the charge of the proton. Substituting the values, we get F = (1.792 N/C) * (1.6 * 10^-19 C) = 2.867 * 10^-20 N.

Therefore, the force on the proton due to the dipole is 2.867 * 10^-20 N, directed towards the dipole along the y-axis. I hope this helps!