Suppose a current carrying wire Is placed in vertical direction. A charged rod is placed is placed nearly horizontally.It is clear that magnetic field due to current carrying wire is inside the paper.So,We see here that magnetic force acts in upward direction on the charged rod. The force mg lies in downward direction.If we increase the magnitude of current,magnitude of field increases and force increases too. At some value of current, magnetic force exceeds the mg and it seems that the force is doing somekind of work and the rod lifts up. How is it possible when we know that work done by magnetic force is always zero. This question is troubling me for last couple of days. I am in a highschool student and we just have completed the magnetism chapter.

• If the current is changing, then the magnetic field is changing, and that induces an electric field according to Faraday's Law. Perhaps that law will come along in the next chapter or two, but you can look ahead now. – MikeV Aug 11 '15 at 13:23
• How do u mean? Will the induced electric field cancel out magnetic field anyway? – Mohammad Abid Aug 14 '15 at 8:45
• AS @gleedadswell points out, there is no magnetic force on the charged rod while (i) the magnetic field is constant and (ii) the rod is not moving. BTW, the magnetic field is into the paper only to the right of the vertical wire -- it is out of the paper to the left of the rod. – MikeV Aug 15 '15 at 12:31
• What if two current carrying wires carrying constant currents are kept in same vertical planes. The force is attractive and work done by magnetic again seems +ve. – Mohammad Abid Aug 15 '15 at 13:20

How is the magnetic field exerting a force on the charged rod? Magnetic fields exert forces on moving charges, not on stationary ones.

As @MikeV points out, if the magnetic field is changing then it induces an electric field. This can exert a force on the charged rod. But for a single current carrying wire to exert any significant induced force on a charged rod the rate of change of the current in the wire would have to be enormous.

I don't think in your question you are thinking about induced fields, though. You say

At some value of current, magnetic force exceeds the mg and it seems that the force is doing somekind of work and the rod lifts up

The "At some value of current" statement seems to indicate that you think the magnetic field exerts a force on the charged rod. It doesn't. You can't lift a rod this way.

• What if two current carrying wires carrying constant currents are kept in same vertical planes. The force is attractive and work done by magnetic again seems +ve. – Mohammad Abid Aug 14 '15 at 8:44
• The force between the wires is attractive if the wires are parallel and the current runs in the same direction in both (it is repulsive if the currents are opposite). You can lift a wire this way (it is, in fact a common undergraduate experiment) but you need a very big current to exert a relatively small magnetic force. However, with coils instead of straight wires you can start to get some significant forces. – gleedadswell Aug 18 '15 at 3:30
• Perhaps yes, but the question remains as it was although maybe practically not possible but going mathematically it seems that work done is positive which is something not realizable as maths does prove physics right? – Mohammad Abid Aug 19 '15 at 15:13
• @MohammadAbid I don't understand your comment. There is no contradiction between the physics and the math. Two wires can do work on each other, but a magnetic field does no work on a free moving charge. The math (in the physical theory) says so and experiment confirms it. – gleedadswell Aug 20 '15 at 2:28
• You are missing a very important point. I am making a large distinction. The (magnetic) forces that wires exert on each other is one thing that I am talking about. For the wires elementary definitions of work allow us to conclude that can do work on each other. On the other hand if we are talking about the (magnetic) force on a free particle (e.g. an electron moving through a vacuum) then the form of the magnetic force, $\vec{F}_B = q\vec{v} \times \vec{B}$ leads us to the conclusion that the magnetic force can do no work on this charge. These are very different cases. – gleedadswell Aug 20 '15 at 23:46