The magnetic field on the axis of a circular current loop (eq. 5.41) is far from uniform (it falls off sharply with increasing z). you can produce a more nearly uniform field by using two such loops a distance d apart (fig. 5.59). (a) find the field (b) as a function of z, and show that ∂b/∂z is zero at the point midway between them (z = 0). (b) if you pick d just right, the second derivative of b will also vanish at the mid- point. this arrangement is known as a helmholtz coil; it’s a convenient way of producing relatively uniform fields in the laboratory. determine d such that ∂2 b/∂z2 = 0 at the midpoint, and find the resulting magnetic field at the center. √ [ 8μ0i/5 5r]

Part b

Explanation:

Part a)

Let the radius of the coil is R and magnetic field on its axis is given as

now we know that two coils are identical and we need to find magnetic field between two coils

so we will have net magnetic field given as

Now we know that magnetic field is maximum at position

so we will have

so it will be at mid point of two coils

Part b)

Now we know that

so we will have

now magnetic field is given as

put z = 0.5 R

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