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https://texercises.com/exercise/helmholtz-coil/
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Exercise:
The magnetic field along the axis of a Helmholtz coil with radius rO and NO turns per coil is measured to be BHO. abcliste abc Calculate the current through the coils. abc The distance between the coils is increased to dO while keeping the current constant. Calculate the magnetic field in the middle between the two coils. abcliste

Solution:
abcliste abc The magnetic field in a Helmholtz coil is given by sscBH mu_leftfracright^fracfracN Ir Solving for the current I leads to I leftfracright^fracfracsscBH rmu_ N leftfracright^fractimesfracBHtimes rncmuotimes N I approx resultIP abc The distance corresponds to twice the radius d r. For a single coil the magnetic field at a distance r from its centre can be calculated as B_r fracmu_fracN I r^leftr^+r^right^frac fracmu_fracN I r^left r^right^frac fracmu_fracN I r^^frac r^ fracmu_ ^fracfracN Ir fracmu_ leftfracright^fracfracN Ir For both coils together the magnetic field at the centre is given by sscBtot BF ncmuotimes leftfracright^fractimesfracNtimes Ir B approx resultBP- abcliste
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Exercise:
The magnetic field along the axis of a Helmholtz coil with radius rO and NO turns per coil is measured to be BHO. abcliste abc Calculate the current through the coils. abc The distance between the coils is increased to dO while keeping the current constant. Calculate the magnetic field in the middle between the two coils. abcliste

Solution:
abcliste abc The magnetic field in a Helmholtz coil is given by sscBH mu_leftfracright^fracfracN Ir Solving for the current I leads to I leftfracright^fracfracsscBH rmu_ N leftfracright^fractimesfracBHtimes rncmuotimes N I approx resultIP abc The distance corresponds to twice the radius d r. For a single coil the magnetic field at a distance r from its centre can be calculated as B_r fracmu_fracN I r^leftr^+r^right^frac fracmu_fracN I r^left r^right^frac fracmu_fracN I r^^frac r^ fracmu_ ^fracfracN Ir fracmu_ leftfracright^fracfracN Ir For both coils together the magnetic field at the centre is given by sscBtot BF ncmuotimes leftfracright^fractimesfracNtimes Ir B approx resultBP- abcliste
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Branches
Magnetism
Tags
coil, current, helmholtz coil, magnetic field
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Decoration
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