Question

A dipole moment, p = (2 Cm i) + (-5 Cm j) + (7 Cm k), is within an E = (-5 N/C i) + (6 N/C j) + (3 N/C k).

- Determine the potential energy stored by the dipole in the field.
- Determine the torque on the dipole by the field.
- Determine the angle between the dipole moment and the field.

Answer 1

= dipole moment = 2 i - 5 j + 7 k

= electric field = - 5 i + 6 j + 3 k

Potential energy stored by the dipole in the field is given as

U = - .

U = - (2 i - 5 j + 7 k).(- 5 i + 6 j + 3 k)

U = 19 J

Torque on the dipole is given as

= x

= (2 i - 5 j + 7 k) x (- 5 i + 6 j + 3 k)

= - 57 i - 41 j - 13 k

|| = magnitude of torque = = 71.4

|| = magnitude of dipole moment = = 8.83

|| = magnitude of electric field = = 8.4

= angle between electric field and dipole moment

using the equation

(|| ) = (||) ( ||) Sin

71.4 = (8.83) (8.4) Sin

Sin = 0.963

= Sin^-1(0.963)

= 74.4 deg