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Questions 3-23 · Q22

Q.Find the number of oscillations performed per minute by a magnet vibrating in the plane of a uniform field of 1.6×10−51.6\times10^{-5} Wb/m2^2. The magnet has moment of inertia 3×10−63\times10^{-6} kg m2^2 and magnetic moment 3 A m2^2.

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Using the vibration-magnetometer period formula T=2πI/(μB)T=2\pi\sqrt{I/(\mu B)} (Eq. 5.34), with I=3×10−6I=3\times10^{-6} kg m2^2, μ=3\mu=3 A m2^2, B=1.6×10−5B=1.6\times10^{-5} Wb/m2^2: μB=3×1.6×10−5=4.8×10−5, so IμB=3×10−64.8×10−5=0.0625\mu B=3\times1.6\times10^{-5}=4.8\times10^{-5}\text{, so } \frac{I}{\mu B}=\frac{3\times10^{-6}}{4.8\times10^{-5}}=0.0625 T=2π0.0625=2π(0.25)=1.5708 sT=2\pi\sqrt{0.0625}=2\pi(0.25)=1.5708\text{ s} Number of oscillations per …

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