Mindscrape said:Hmm, in your way after you crank through it all you find that [itex]\mathbf{E} \times(\nabla \times \mathbf{p})=-(\mathbf{E}\cdot\nabla)\mathbf{p}[/itex]? If that is true then you are okay, and it seems like an acceptable solution.
Mindscrape said:Hmm, in your way after you crank through it all you find that [itex]\mathbf{E} \times(\nabla \times \mathbf{p})=-(\mathbf{E}\cdot\nabla)\mathbf{p}[/itex]? If that is true then you are okay, and it seems like an acceptable solution.
As far as the other solution goes, it's probably the picture that is screwing you up, in the picture zhat is pointing out of the page, and the electric field wants to torque the the dipole to line up with it, so it wants to torque the dipole into the zhat direction. "We" are rotating the dipole clockwise, the way it wants to go, so we are doing negative work.
neelakash said:The solution is post possibly is not correct.
ehrenfest said:Homework Statement
This question refers to Griffiths E and M book.
See the solution here http://www.physics.gatech.edu/academics/Classes/fall2005/3122/hw9solution.pdf
I don't understand why they say the torque we exert is clockwise (I assume that means in the minus z direction).
Homework Equations
The Attempt at a Solution
Griffiths E&M refers to the textbook "Introduction to Electrodynamics" by David J. Griffiths, which covers the principles of electromagnetism. Understanding torque direction is important in many areas of physics and engineering, as it allows us to predict the rotational motion of objects.
Torque direction is related to electromagnetism because it involves the interaction between electric and magnetic fields. In the context of Griffiths E&M, torque direction is often discussed in the context of a current-carrying loop in a magnetic field, where the torque on the loop is determined by the direction of the magnetic field and the direction of the current.
The direction of torque on an object is affected by several factors, including the direction and strength of the magnetic field, the direction of the current, and the orientation of the object with respect to the magnetic field. In addition, the shape and size of the object can also affect the torque direction.
The direction of torque can be found using the right-hand rule, which states that if you point your thumb in the direction of the current and your fingers in the direction of the magnetic field, the direction your palm faces will indicate the direction of the torque. This rule can be applied to current-carrying loops or other situations involving electromagnetism.
Understanding torque direction is crucial in many practical applications, such as designing motors, generators, and other electromechanical devices. It also plays a role in the operation of electric motors and generators, as well as in the production of electricity through electromagnetic induction. Additionally, understanding torque direction can help in the analysis and prediction of the behavior of objects in magnetic fields.