The design of a magneto-optical atom trap requires a magnetic field B that is di

Question

The design of a magneto-optical atom trap requires a magnetic field B that is directly proportional to position x along an axis. Such a field perturbs the absorption of laser light by atoms in the manner needed to spatially confine atoms in the trap. Let us demonstrate that "anti-Helmholtz" coils will provide the required field B=Cx, where C is a constant. Anti-Helmholtz coils consist of two identical circular wire coils, each with radius 3.9 cm and 140 turns, carrying current I in opposite directions (the figure). The coils share a common axis (defined as the x axis with x=0 at the midpoint (0) between the coils). Assume that the centers of the coils are separated by a distance equal to the radius 3.9 cm of the coils. (Figure 1)

For optimal atom trapping, dB/dx should be about 0.15T/m. Assume an atom trap uses anti-Helmholtz coils with R = 3.9 cm and N = 140. What current should flow through the coils? Constant C=48?0NI/255?R2. [Coil separation equal to coil radius, as assumed in this problem, is not a strict requirement for anti-Helmholtz coils.]

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Given B=Cx and C=48u0*N*I/255*R, R=.039m and N=140

Now db/dx=d/dx(Cx)

db/dx=C

Given db.dx=0.15T/m

Sp 0.15=48u0*140*I/255*.039

I=0.15*255*.039*10^7/48*140*4*pi

I=176.74 Amp

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