A force of 4.3 x 10-15 N acts between an electric dipole with dipole moment 2.3 x 10-29 C m and an electron.
How far away from the dipole is the electron located when it travels along the dipole axis?
Find E for the dipole at some distance r.
dipolemoment= qd where q is the charge, and d is the separtation. So q= 2.3E-29/d
E= kq(1/(r-d/2)^2 -1/(r+d/2)^2)
ok, combine those, knowing q= 2.3E-29/d
Some algebra is required. It is not hard.
It should reducte to something like
E= k 2.3E-29/r^3
Now force is Ee where e is the charge on an electron.
Solve for r.
The electric field at a distance r from a dipole of moment p, at a point that is located along the axis of the dipole, is E(r) = [2/(4 pi epsilono)]* p/r^3
You should be able to find this equation in your textbook or notes somewhere, or on the internet. Usually it is in vector form, because the force depends upon dipole orientation as well as separation. The equation abobe is from the text of Reitz and Milford
Set e*E(r) = 4.3 x 10-15 N and solve for the separation,r.
1/(4 pi epsilono) is often abbreviated as the "Coulomb constant" , k
they gave u qd which is dipole moment.
They gave u F (in N).
E=qd/2pi(e0)x^3
e0 is a constant (8.55*10^-12)
E=F/charge of electron
isolate for x^3= #
cube root that number and now u have distance in meters.
To find the distance at which the electron is located from the dipole, we can use Coulomb's Law for the force between two charges:
F = k * (q1*q2) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
In this problem, the dipole moment of the electric dipole is given as 2.3 x 10^-29 C m. This means that the magnitude of the charge (q1 or q2) is equal to 2.3 x 10^-29 Coulombs.
The force acting between the dipole and the electron is given as 4.3 x 10^-15 N.
Let's use the above equation to solve for the distance (r):
4.3 x 10^-15 N = (8.99 x 10^9 N m^2/C^2) * (2.3 x 10^-29 C)^2 / r^2
Simplifying:
r^2 = (8.99 x 10^9 N m^2/C^2) * (2.3 x 10^-29 C)^2 / (4.3 x 10^-15 N)
r^2 = (8.99 x 10^9 N m^2/C^2) * (2.3 x 10^-29 C)^2 / (4.3 x 10^-15 N)
r^2 ≈ 9.53 x 10^-6 m^2
Taking the square root of both sides:
r ≈ 9.76 x 10^-3 m
Therefore, the electron is located approximately 9.76 x 10^-3 meters away from the dipole when it travels along the dipole axis.