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Permanent Magnets — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsPermanent Magnets4 Marks
Question
A short magnet makes 40 oscillations per minute when used in an oscillation magnetometer at a place where the earth's horizontal magnetic field is $2\mu\text{T.}$ Another short magnet of magnetic moment 1.6A-m2 is placed 20cm east of the oscillating magnet. Find the new frequency of oscillation if the magnet has its north pole:
  1. Towards north.
  2. Towards south.
✓

Answer

$\gamma_1=40$ oscillations/ minute

$\text{B}_\text{H}=25\mu\text{T}$

m of second magnet = 1.6A-m2

d = 20cm = 0.2m

For north facing north

$\gamma_1=\frac{1}{2\pi}\sqrt{\frac{\text{MB}_{\text{H}}}{\text{I}}}$

$\gamma_2=\frac{1}{2\pi}\sqrt{\frac{\text{M}(\text{B}_{\text{H}}-\text{B})}{\text{I}}}$

$\text{B}=\frac{\mu_0}{4\pi}\frac{\text{m}}{\text{d}^3}=\frac{10^{-7}\times1.6}{8\times10^{-3}}=20\mu\text{T}$

$\frac{\gamma_1}{\gamma_2}=\sqrt{\frac{\text{B}}{\text{B}_{\text{H}-\text{B}}}}\Rightarrow\frac{40}{\gamma_2}=\sqrt{\frac{25}{5}}\Rightarrow\gamma_2=\frac{40}{\sqrt{5}}$

$=17.88\approx18\text{ osci/min}$ 

For north pole facing south

$\gamma_1=\frac{1}{2\pi}\sqrt{\frac{\text{MB}_{\text{H}}}{\text{I}}}$

$\gamma_2=\frac{1}{2\pi}\sqrt{\frac{\text{M}(\text{B}_{\text{H}}-\text{B})}{\text{I}}}$

$\frac{\gamma_1}{\gamma_2}=\sqrt{\frac{\text{B}}{\text{B}_{\text{H}-\text{B}}}}\Rightarrow\frac{40}{\gamma_2}=\sqrt{\frac{25}{45}}\Rightarrow\gamma_2=\frac{40}{\sqrt{\Big(\frac{25}{45}\Big)}}$

$=53.66\approx54\text{ osci/min}$

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