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Question

Radius of current carrying coil is R. If fractional decreases in field value with respect to centre of the coil for a near by axial point is 1% then find axial position of that point.

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Solution

Fractional decrease in magnetic field along the axis at a distance x from the center of coil is 1%.

Magnetic field on the axis μoiR22(x2+R2)3/2

Magnetic field on the center, Bcenter=μoi2R

ΔB=1%Bcenter

μoi2RμoiR22(x2+R2)3/2=1100 μoi2R

0.99μoi2R=μoiR22(x2+R2)3/2

R30.99=(x2+R2)3/2

(R30.99)2/3=x2+R2

x2=R20.992/3R2

x=±0.082R

At distance x=±0.082R from center Magnetic field change is 1% with respect to magnetic field at center.


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