A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the ele

Question

A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes from:

Accepted Answer

1. **Diamagnetic Repulsion:** Diamagnetic substances are repelled by magnetic fields and tend to move from the stronger part of the field to the weaker part . This repulsion lifts the rod against gravity.
2. **Work Done by Magnetic Field:** A fundamental principle in magnetism is that the magnetic force ($F_m = q(\mathbf{v} 	imes \mathbf{B})$) acts perpendicular to the velocity of a charge and therefore does **no work** on the charge . While the macroscopic force on a dipole seems to do work, the energy balance in a system involving electromagnets must be traced back to the energy supply.
3. **Energy Conservation:** When the rod moves upwards, it gains gravitational potential energy. This energy cannot come from the static magnetic field itself (which doesn't do work) nor the lattice. The movement of the magnetic material changes the magnetic flux linked with the electromagnet's coils. To maintain the steady current in the electromagnet against the resulting back EMF (induced due to the rod's motion/change in flux), the **current source** (battery/power supply) must do extra work. Thus, the energy required to lift the rod is supplied by the current source.
4. **Induced Electric Field:** While a changing magnetic field induces an electric field (Faraday's Law) which is responsible for creating the induced diamagnetic moment (via the change in orbital speed of electrons, akin to Lenz's law) , the continuous supply of energy for macroscopic mechanical work is attributed to the source maintaining the field.

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