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Question: 1 if you have a single circular coil of radius...

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1. If you have a single circular coil of radius R, lying in the ry-plane and centered around the origin, the magnetic field along the z axis, B(z), is maximized at z = 0 (8B/Oz = 0 here). Suppose instead you have two such coils with centers on the z-axis, with parallel and equal currents, lying in planes at locations z td/2. (a) Write down an expression for B(2), the magnetic field along the z axis due to the two loops. Assume the currents are moving in a direction such that B(z) 〉 0. (b) Find OB/oz and verify it equals zero at z 0 (the field is maximized at z-0). (c) Taylor expand your expression for дв/az around z-: 0 and keep the leading nonzero order in z (this should be something times z1) (d) Using your expression from part (c), fino 2B/0z2 at z-0. For a particular value of d, the second derivative of B(z) can equal zero as well as the first derivative. Find this value of d. This arrangement is called a Helmholtz coil, producing a very uniform magnetic field in the region between the coils.

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