Electric fields - dipole moment

[Predator]

Homework Statement

An electric dipole, consisting of charges of magnitude 2.60 nC separated by 7.20 µm, is in an electric field of strength 1400 N/C.

(a) What is the magnitude of the electric dipole moment?

(b) What is the difference in potential energy corresponding to dipole orientations parallel to and antiparallel to the field?

Homework Equations

p = dipole moment = q * d

U = -p * E

The Attempt at a Solution

For a), it's just plug and chug.

q = 2.6 * 10^-9C
d = 7.2 * 10^-6m

q*d = 1.87E-14

For b), I'm assuming we use U = -p * E.

So for parallel, it's -pE but then what does antiparallel mean? That just means its not parallel right? (doesn't imply that its perpendicular does it?)

 

[anathema]

Hi there!

Great job on finding the magnitude of the electric dipole moment. For part (b), you are correct that we can use the equation U = -p * E. For the orientation parallel to the field, the dipole moment and the electric field are in the same direction, so the potential energy would be negative. However, for the antiparallel orientation, the dipole moment and the electric field are in opposite directions, so the potential energy would be positive. This is because the electric field would be doing work on the dipole to align it in the opposite direction, resulting in an increase in potential energy. So, the difference in potential energy would be the sum of the two values, or 2pE. I hope this helps!

 

[Moetasim]

Your approach is correct for part a) of the problem. The magnitude of the electric dipole moment is equal to the product of the charges and the distance between them, which in this case is 1.87 x 10^-14 Cm.

For part b), you are correct in using the equation U = -p * E. Antiparallel means that the dipole is oriented in the opposite direction of the electric field. In this case, it would mean that the negative charge is facing the positive end of the electric field and vice versa. This would result in a negative potential energy, since the negative sign in the equation indicates that the potential energy is in the opposite direction of the electric field. So for the antiparallel orientation, the potential energy would be -(-1.87 x 10^-14 Cm)(1400 N/C) = 2.61 x 10^-11 J. This is the difference in potential energy between the parallel and antiparallel orientations.