The torque on a dipole in an external electric field is expressed as τ = p × E, where τ is torque, p is the dipole moment, and E is the electric field. This expression arises from the vector nature of torque, which is defined as the cross product of the dipole moment and the electric field. The discussion emphasizes that the order of the cross product matters, as A × B is not equal to B × A, leading to different directions for torque based on the chosen coordinate system. Understanding these vector relationships is crucial for accurately describing the behavior of dipoles in electric fields.
PREREQUISITESStudents of physics, particularly those studying electromagnetism, as well as educators and researchers interested in the dynamics of dipoles in electric fields.
What's the essential difference in the cross products A x B versus B x A?Prashasti said:Homework Statement
Why isn't the expression for torque on a dipole kept in an external electric field ExP? Why is it PxE?
No such indication has been given in any of the derivations, that it is mandatory for it to be PxE, so why can't it be ExP?
2. The attempt at a solution
Is it all about experiments?
Right. So it comes down to the definitions of positive or negative directions for quantities in the chosen coordinate system. This includes assumed directions for positive or negative torques, angular velocities, etc., which are vector quantities (or pseudo vector quantities in some cases, but that's another topic).Prashasti said:The direction of the resultant of A x B is just opposite to that of B x A...