An electric dipole consisting of charges of magnitude 1.70 nC separated by 6.80 μm is in an electric field of strength 1160 N/C. What are (a) the magnitude of the electric dipole moment and (b) the difference between the potential energies for dipole orientations parallel and antiparallel to Upper E Overscript right-arrow EndScripts?

p = 1.16 10⁻¹⁴ C m and ΔU = 2.7 10 - 11 J

Explanation:

The dipole moment of a dipole is the product of charges by distance

p = 2 a q

With 2a the distance between the charges and the magnitude of the charges

p = 1.7 10⁻⁹ 6.8 10⁻⁶

p = 1.16 10⁻¹⁴ C m

The potential energie dipole is described by the expression

U = - p E cos θ

Where θ is the angle between the dipole and the electric field, the zero value of the potential energy is located for when the dipole is perpendicular to the electric field line

Orientation parallel to the field

θ = 0º

U = 1.16 10⁻¹⁴ 1160 cos 0

U1 = 1.35 10⁻¹¹ J

Antiparallel orientation

θ = 180º

cos 180 = - 1

U2 = - 1.35 10⁻¹¹ J

The difference in energy between these two configurations is the subtraction of the energies

ΔU = | U1 - U2 |

ΔU = 1.35 10-11 - (-1.35 10-11)

ΔU = 2.7 10 - 11 J