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a) Consider a current loop of radius a in the ry plane, carrying a steady current I. Using the Biot-Savart law, show that the B field along the rotation axis of the loop is B(z) = Hola² 2(a² + z²)3/2 ez. [6] b) Now consider a pair of current loops with the same radius a and current I and a common rotation axis lying along the z axis, with their centres at z = -d and z = d. Write down the resulting B field along the axis and determine the far field limit (z » a, z » d) for B₂ along the axis. Sketch the field lines in the xz plane. c) At z = 0, determine B, and its derivatives and JB₂ дz 8² B₂ əz² Determine the ratio d/a 8² B₂ for which əz² vanishes. [8] d) Find the force between the two loops. You should use F = V(m B), where m is the magnetic dipole moment of one current loop, and B the magnetic field of the other loop. Is the force attractive or repulsive? [7]