Two identical, flat, circular coils of wire each have N turns and radius R. The

Question

Two identical, flat, circular coils of wire each have N turns and radius R. The coils are arranged as a set of Helmholtz coils so that the separation distance between the coils is equal to the radius of the coils as shown in Fig. 5. Each coil carries current I. The magnitude of the magnetic field at a point on the common axis of the coil and halfway between them is BR. If the separation distance increases 4R, how much does the magnitude of the magnetic field decreases at a point on the common axis of the coil halfway between them?

Problem 7. (4 points) Helmholtz coils: Magnetic field due to two circular coils. Two identical, flat, circular coils of wire each have N turns and radius R. The coils are arranged as a set of Helmholtz coils so that the separation distance between the coils is equal to the radius of the coils as shown in Fig. 5. Each coil carries current I. The magnitude of the magnetic field at a point on the common axis of the coil and halfway between them is BR. If the separation distance increases 4R, how much does the magnitude of the magnetic field decreases at a point on the common axis of the coil halfway between them? (A) 2 times smaller (B) 4 times smaller (C) 6 times smaller (D) 8 times smaller Figure 5. Helmholtz coils.

Explanation / Answer

Here magnetic field is given by

B = 2*u0/2* iR^2 /(z^2 +R^2)

Initially z=R/2 and finally it becomes 4R/2

So denominator in first case = 1.25^1.5 R^3

Denominator in second case = 5^1.5 R ^3

Now ratio of denominators (5/1.25)^1.5 = 8

So it becomes 8 times smaller.

  

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