Electromagnetic induction and magnetic field (conducting rail problem)

Since we know the work done by a magnetic field is zero.now how does the magnetic field changes the kinetic energy of rod when it applies force BIL (where I is current at any instant)

moreover if we apply if we apply some external force which balances the magnetic force the work done by both force will be 0(their sum) ,however we know induced current flows in circuit due to motional emf of rod and energy is lost through resistance where does this energy come from?(since no work is done)

• This is hard to understand. Could you please use shorter sentences? – Philip Wood Aug 7 '18 at 18:20
• should i edit it ? did u understand its about conducting bars kept on parallel conducting rails – Akshat Gautam Aug 7 '18 at 18:24
• Yes, I understand the set-up, but you seem to be cramming many ideas into each sentence, and it isn't too clear exactly what you're asking. – Philip Wood Aug 7 '18 at 18:27
• well i tried to simplify it – Akshat Gautam Aug 7 '18 at 18:35
• You did well. Much clearer. – Philip Wood Aug 7 '18 at 21:37

1 Answer

if we make the current flow through rod the rod will experience force BIL and thus its kinetic energy will change that contradicts work energy theorem

No, it doesn't. Ponderomotive forces (or Laplace forces) act on the conductor and they can do work. The Lorentz force $q\mathbf v\times\mathbf B$ acts on the charge carriers and does no work on them. But these forces do not act on the conductor (wire, rod) directly. Other forces due to charge carriers act on the conductor, which together form the macroscopic force of magnitude $BIL$. This macroscopic force, of course, does work.

• well then if i oppose this force with an equal and opposite force where does the energy lost through resistance come from(assuming rod is moving with constant velocity) – Akshat Gautam Aug 7 '18 at 18:38
• From the chemical energy in the voltage source. This energy is changed into macroscopic EM energy right near the source, then it flows directed by the wires from the voltage source, along the wires, into the rod. Then in the wires and in the rod which have non-zero electric resistance this energy is transformed into kinetic energy of the chaotic motion of the particles - so-called Joule losses. – Ján Lalinský Aug 7 '18 at 18:41
• if there is no original voltage source(which means current is only through induced emf) – Akshat Gautam Aug 7 '18 at 18:43
• Then the rod has to be pushed by external mechanical force. The source of this force supplies energy both for accelerating the rod and for the heat generated by induced currents. – Ján Lalinský Aug 7 '18 at 20:02
• thanks but i'm still having confusion in the case in which we apply a external mechanical force which is exactly equal to magnetic force which will make the rod with a constant velocity say v the induced current will be still there and so heat will be lost but now the net work is zero – Akshat Gautam Aug 8 '18 at 18:02