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Imagine a circular wire loop of radius R carrying current I, suspended above a current carrying solenoid in the non-uniform magnetic field of the solenoid. Here, $\vec{B}$ has a radial component as the magnetic field, to a good approximation, radiates spherically.

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It is claimed there is a downward force on the loop.

Why is this so? What is happening?

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  • $\begingroup$ The 'suspended loop' is depicted with the letter "I" and an arrow. Why? Also, you speak of 'nonuniform magnetic field'; could this be a time-dependent (changing) magnetic field? $\endgroup$ – Whit3rd Sep 2 '16 at 1:02
  • $\begingroup$ @Whit3rd Page 273 117.55.241.6/library/E-Books/… $\endgroup$ – Physkid Sep 2 '16 at 1:17
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Parallel currents attract. The solenoid, with current in the direction shown, has current parallel to that in the loop, and the loop will be attracted to the solenoid. A uniform B field, however, would put no net force on such a loop; any force on one section of the loop would be cancelled by equal and opposite force on another section of the loop (the opposite side of the loop carrying the same current in the opposite direction).

The radial (radiating as if it were coming from a point in the center) B field component is not uniform (it's strong in the center, and points in various directions). That part of the B field puts a net force on the current-carrying ring.

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