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https://texercises.com/exercise/helmholtz-coil-non-uniformity/
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Exercise:
The field along the axis of a Helmholtz coil is approximately constant but not completely. Calculate the percentage decrease from the midpo between the coils to the centre of one of the coils.

Solution:
The magnetic field at the midpo between the pos is B_M fracmu_ fracN I r^leftr^+r/^right^/leftfracright^/mu_fracN Ir The field at the centre of a coil is B_C B+Br fracmu_fracN Ir+fracmu_fracN I r^leftr^+r^right^/ fracmu_ N Ileftfracr+fracr^left r^right^/right fracmu_fracN Irleft+frac^/right fracmu_fracN Irleft+fracsqrtright mu_fracN Irfrac+sqrt It follows for the ratio fracB_CB_M fracfrac+sqrtleftfracright^/ fracsqrt+sqrt resultratioP The magnetic field decreases by changeP from the middle between the coils to the centre of a coil.
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Exercise:
The field along the axis of a Helmholtz coil is approximately constant but not completely. Calculate the percentage decrease from the midpo between the coils to the centre of one of the coils.

Solution:
The magnetic field at the midpo between the pos is B_M fracmu_ fracN I r^leftr^+r/^right^/leftfracright^/mu_fracN Ir The field at the centre of a coil is B_C B+Br fracmu_fracN Ir+fracmu_fracN I r^leftr^+r^right^/ fracmu_ N Ileftfracr+fracr^left r^right^/right fracmu_fracN Irleft+frac^/right fracmu_fracN Irleft+fracsqrtright mu_fracN Irfrac+sqrt It follows for the ratio fracB_CB_M fracfrac+sqrtleftfracright^/ fracsqrt+sqrt resultratioP The magnetic field decreases by changeP from the middle between the coils to the centre of a coil.
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Magnetism
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electromagnet, helmholtz coil
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(3, default)
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Language
ENG (English)
Type
Calculative / Quantity
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