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Exercise:
Show that the field at the centre of a Helmholtz coil corresponds to the of the fields produced by two circular loops with a common axis placed at a distance d  r where r is the radius of the coils.

Solution:
The field produced by a single current loop with radius r current I and N turns is given by Bz fracmu_ fracN I r^left r^ + z^ right^/ In a Helmholtz setup the centre has a distance of zr/ to each of the two coils. The field at the centre is thus sscBHelmholtz Br/ fracmu_ fracN I r^left r^ + r/^ right^/ mu_ fracN I r^left r^ + r^/ right^/ mu_ fracN I r^leftfrac r^ right^/ mu_ fracN I r^leftfracright^/ r^ mu_ leftfracright^/ fracN Ir
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Exercise:
Show that the field at the centre of a Helmholtz coil corresponds to the of the fields produced by two circular loops with a common axis placed at a distance d  r where r is the radius of the coils.

Solution:
The field produced by a single current loop with radius r current I and N turns is given by Bz fracmu_ fracN I r^left r^ + z^ right^/ In a Helmholtz setup the centre has a distance of zr/ to each of the two coils. The field at the centre is thus sscBHelmholtz Br/ fracmu_ fracN I r^left r^ + r/^ right^/ mu_ fracN I r^left r^ + r^/ right^/ mu_ fracN I r^leftfrac r^ right^/ mu_ fracN I r^leftfracright^/ r^ mu_ leftfracright^/ fracN Ir
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Tags
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Difficulty
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Points
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Language
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Type
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