# Magnetic field

If magnetic field does not do any work then how is it that magnets are able to lift iron filings and cause electrons to move (hence causing current to flow) when a metal is dragged through a uniform magnetic field? Could someone please explain

Also why do magnetic field lines form closed loops but not electric field lines?

Note by Pranav Chakravarthy
5 years, 5 months ago

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$$W = F \cdot s = Fs \cos \theta$$

There is displacement, but not in direction of the force applied, hence $$\theta = 90 deg \Rightarrow W = 0$$

- 5 years, 5 months ago

Griffith's Introduction to Electrodynamics 3rd ed. has a pretty good discussion of this on pages 209-210 of how it can seem like the magnetic force is performing work in some cases but in fact it isn't. His example is a little too long to repeat here, but it's basically this: as soon as a current carrying wire in a magnetic field moves in response to the magnetic force on it, the velocity of the charge carriers in the wire now has a component perpendicular to the wire, so the Lorentz force has component back along the wire. Whatever counters this backward force to maintain the current during the motion is what is truly doing the work.

The case of permanent magnets doing work has always bothered me. I've never found a good explanation. Presumably it is really electric forces inside the materials doing work; they somehow maintain the microscopic currents as the materials move toward one another.

Saying magnetic field lines form closed loops is another way of stating Gauss' law for magnetism. If we ever discover magnetic monopoles, we'd have an exception. Electric field lines can form closed loops but only if there is a changing magnetic flux through those loops. A collection of static charges can't make an electric field line that is a loop. Imagine if there were. You could make a looped tube that followed the field and put a few electrons in. They would loop around faster and faster and faster as they're pushed by the field, gaining more and more kinetic energy. This would violate conservation of energy.

- 5 years, 5 months ago

how the magnetic field hold the world?

- 4 years, 11 months ago

Magnetic field doesn't do any work only because the force is perpendicular to the motion of electron. And as Harshit said F.S IS ZERO.

But as far as the work done in moving metal being dragged is concerned, it is not the work done by the magnetic field but it is due to the work done by the external force that we apply on the rod to move. (Oviously you have to apply force to move the conductor).

As far as the work done on the iron filings is concerned, it does not have any thing to do with moving charges.Hence the work is done in this case.

Remember the work done by magnetic field is zero only when charges are moving in magnetic field not otherwise (like iron filings).

- 5 years, 5 months ago

I'm not 100% sure, but I a guess is that the reason magnetic field lines form closed loops but electric field lines doesn't is because a magnet is always (from what we know today) a dipole, i.e. it has both a north and a south. Electric charges though are often monopoles (only + or -), and thereby their electric field lines don't form loops. As I said, I'm not sure this is totally correct, and if it's not, the users of Brilliant are welcome to correct me.

- 5 years, 5 months ago