Answer to Question #88360 in Electricity and Magnetism for Grace

Question

A dipole with a dipole moment of strength p= 5.64*10^-4 Cm is located D= 0.71 m away from a grounded plane conducting surface. The direction of the dipole moment is perpendicular to the conducting surface. Calculate the strength of the translational force on the dipole with positive values indicating a force away from the surface and negative values a force toward the surface. The displace between the charges forming the dipole is much smaller than the distance of the dipole from the surface.

Answer 1

The translational force F is given by formula

$$F=E \times D (1)$$

where E is the strength of the field

The strength of the field

$$E=\frac {1} {4\pi ɛ_0} \frac {p} {D^3} \sqrt{1+3 \cos^2 \theta} (2)$$

where ɛ₀ is the electric constant

In our case,

$$\theta=90°$$

We put (2) in (1):

$$F=\frac {1} {4\pi ɛ_0} \frac {p} {D^2} \sqrt{1+3 \cos^2 \theta} (3)$$

Using (3) we got:

$$F=4 \times 10^7 N$$

Answer:

$4 \times 10^7 N$