The magnitude of the force on a magnetic dipole μ→ aligned with a nonuniform magnetic field in the positive x direction is Fx = |μ→| dB/dx. Suppose two flat loops of wire each have radius R and carry a current I. (a) The loops are parallel to each other and share the same axis. They are separated by a variable distance x >> R. Show that the magnetic force between them varies as 1/x4. (b) Find the magnitude of this force, taking I = 10.0 A, R = 0.500 cm, and x = 5.00 cm.

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