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Question

The magnetometer of the previous problem is used with the same magnet in Tan-B position. Where should the magnet be placed to produce a 37° deflection of the needle?

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Solution


Given:
Deflection in the magnetometer in the given position when placed in the magnetic field of a short magnet, θ = 37°
Separation between the magnet and the needle, d = 10 cm = 0.1 m
Let M be the magnetic moment of the magnet and BH be Earth's horizontal magnetic field.
According to the magnetometer theory,
MBH=4πμ0d2-l222dtan θ For the short magnet,MBH=4πμ0×d42dtan θMBH=4π4π×10-7×0.132×tan 37°MBH=0.5×0.75×1×104MBH=3.75×103 A-m2/T
= 3.75 × 103 A-m2/T
Deflection in the magnetometer θ = 37°
From the magnetometer theory in Tan-B position, we have
MBH=4πμ0d2+l23/2 tan θ
Since for the short magnet l << d, we can neglect l w.r.t. d.
Now,
MBH=4πμ0d3 tanθ3.75×103=110-7×d3×0.75d3=3.75×103×10-70.75 =5×10-4d=5×10-43d=0.079 m=7.9 cm
Magnet will be at 7.9 cm from the centre.

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