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Helmholtz coils consist of two thin flat coils placed as shown in Fig. 27.6. Compare the magnetic field intensities in the centre of each coil with that in the midpoint of the axis and prove that inside the Helmholtz coils the field is almost uniform. Take the distance between the coils to be equal to one half of the radius.

Answer»


Solution :Making use of the result of Problem 27.4, we obtain for the FIELD at the centre of the ring `R_(c)=(mu_(0) iwa^2)/(2) (1/a^(3)+1)/((a^(2)+a^(2)//4)^(3//2))=(mu_(0) iwa^2)/(2a^3) (1+8/sqrt25)=(0.858mu_(0) iw)/(a)`
The field induction at the midpoint is `B_(m)=(2mu_(0) iwa^2)/(2(a^2+a^2//16)^(3//2))=(0.913mu_(0) iw)/(a)`
It may be SEEN that with a SMALL error `delta` the field is almost uniform.
`delta=(B_(m)-B_(c))/(B_(m))=(0.913-0.858)/(0.913)=6%`


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