Derive the expression for the torque acting on a dipole in an external electric field.
Understand the Problem
The question is asking to derive the equation for the torque on an electric dipole when it is placed in an external electric field. This involves using the definition of torque as a force applied at a distance and the force on a charge in an electric field.
Answer
The torque on a dipole in an external electric field is \(\tau = p \times E\) or \(\tau = pE \sin(\theta)\).
The torque ( (\tau) ) acting on a dipole in an external electric field is given by the formula (\tau = p \times E), where (p) is the dipole moment and (E) is the electric field strength. This can also be expressed as (\tau = pE \sin(\theta)), where (\theta) is the angle between the dipole moment and the electric field.
Answer for screen readers
The torque ( (\tau) ) acting on a dipole in an external electric field is given by the formula (\tau = p \times E), where (p) is the dipole moment and (E) is the electric field strength. This can also be expressed as (\tau = pE \sin(\theta)), where (\theta) is the angle between the dipole moment and the electric field.
More Information
The torque tends to align the dipole moment with the electric field. When the dipole moment is aligned with the electric field, the torque is zero, and the dipole is in stable equilibrium.
Tips
A common mistake is to forget that torque is a vector quantity and has both magnitude and direction. Also, students may mix up sine and cosine in the formula.
Sources
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