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I have a square loop which carries a steady current as shown below:

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I was able to find the magnetic field at the centre of the square loop to be: $B=\frac{\sqrt{2}\mu_0I}{\pi R}$

My question is there any force acting on the loop?

  • For example does one part of the current-carrying loop exert force on another current-carrying loop.
  • Does the current carrying loop being in a magnetic field (its own in this case) case a force any way
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Parallel wires with currents in opposite directions repel each other due to the created magnetic fields. Your square loop has that case for opposite sides of the square. The forces on the loop due to its own magnetic field will try to convert the square loop to a circular loop due to that repulsion. Whether it can depends on the forces in place to hold the loop to a square.

The net force on the loop as a whole is zero. If not, it could propel itself across the room by virtue of its own magnetic field which would be a form of perpetual motion. Such a scenario would be as ridiculous as a massive body propelling itself across the universe with its own gravitational field.

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