Christopher Moore is an Assistant Professor of Physics at Coastal Carolina University. He lives in Myrtle Beach, SC with his wife and two children.I was looking at search terms that lead people to this website from Google and stumbled across this one: “the work done by the magnetic field on the charged particle during the semicircular trip.” Someone obviously was interested in how much work a magnetic field could “do”, and Google was kind enough to point them to this forum topic. Luckily my response way back in 2005 was accurate. I would like to expand on it here, though, since many students (actually, most of them) get this wrong, and many a crack-pot theory is based on an incorrect premise. The magnetic field does NO work on a charged particle. In fact, the only thing a magnet can do work on is another magnet or a ferromagnetic material.
Work has a specific definition in physics. It is the dot-product of the force and displacement vectors:
For two vectors, the dot-product is given by:
The force on a charge due to a magnetic field is given by the cross-product of the charge’s velocity vector and the magnetic field vector:
Short version: the force vector is perpendicular to both the velocity vector and the magnetic field vector. (BTW, many students miss this one, too: the charge must have a velocity and therefore must be moving for there to be a magnetic force.) The direction of the force is given by the right-hand rule we talk about at great length.
So, back to the definition for work:
The particle is moving in the direction of the velocity, so the displacement vector will be in the same direction. The magnetic force is always perpendicular to the velocity vector, therefore …
.
The magnetic field can do no work on a charge.
hello,
the abve idea is very good.it leads for me a refreshment for the basics
thank u sir
plz i need an answer to this question (ASAP) the question is :
*How a magnet attract metals ?
i mean by this question the following that magnet attract due to the current in atoms due to electron rotaion so i have moving charges this moving
charges the magnet make force on it this force does no work so from where the
metal gain K.E
*also i have anther case in need to be defiend the electrical motor also we gain energy from it by appling magnatic field
and if the electric field do the work i need a prove that the enrgy gain = the
energy supplied by the electric field and an application to low of conservation
of energy
AND THANKS
A magnet does not attract all metals. Try sticking a magnet to a piece of aluminum or some really crappy steel.
Sir i have a little doubt on what you explained above.
You said “The particle is moving in the direction of the velocity, so the displacement vector will be in the same direction”,but actually the particle will experience magnetic forces also,so it will move in a direction resultant of the both (the velocity vector and magnetic force vector) and hence there will be certain angle b/w magnetic force and displacement vector,and hence word done is not zero.
In short what i m saying is magnetic forces are capable of changing direction of charged particle and hence it must have some effect on the work done.
Hoping for your response :)
Nope. By definition, the velocity vector is always perpendicular to the magnetic force vector. Of course, the magnetic field vector and the velocity vector can share some non-perpendicular component, but the nature of the cross-product insures that the magnetic force is perpendicular to both at all times.
You cannot just add an acceleration vector (essentially the force) and a velocity vector. The resultant would be meaningless, having units of m/s*(1+1/s).
An acceleration (such as the change in direction you mention) only indicates the presence of a force, not necessarily that work has been done.
hi this is Arghyadeep from INDIA.IM A STUDENT OF PHYSICS.I just wanted to know that if the work done on the charged particle by a magnet is zero then what is doing the work in case of attraction of a magnetic material.I mean what is the physics behind work done by a magnet in case of ATTRACTION OF A MAGNETIC MATERIAL.
IS THERE ANY RELATION WITH THE EDDY CURRENTS IN CASE OF WORK DONE IN THIS CASE?
I just want to know the real physics behind it.cross and dot products are simple mathematical approach towards the subject.ill be glad if i get an answer.thanks.
HI! I wanted to ask that in the case of motional emf, or more elaborately, when a thin metallic wire is moving with a velocity v in a direction perpendicular to the direction (say downwards into the plane of paper) of magnetic field, there is an induced emf in the wire, which results from the displacement of electrons apparently in the direction of magnetic force. Now this should have some work being done on the electron, but you said above that no work is done? How is it so?