(A) The time period of a vibration magnetometer is given by $T = 2\pi \sqrt{\frac{I}{MB_{H}}}$, where $I$ is the moment of inertia, $M$ is the magneti

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(A) The time period of a vibration magnetometer is given by $T = 2\pi \sqrt{\frac{I}{MB_{H}}}$, where $I$ is the moment of inertia, $M$ is the magnetic moment, and $B_{H}$ is the horizontal component of the earth's magnetic field.From the formula, we see that $T \propto \frac{1}{\sqrt{B_{H}}}$.Given that $T_{A} = 2T_{B}$, we can write the ratio as $\frac{T_{A}}{T_{B}} = 2$.Using the proportionality, $\frac{T_{A}}{T_{B}} = \sqrt{\frac{B_{HB}}{B_{HA}}}$.Substituting the values, $2 = \sqrt{\frac{32 \times 10^{-6}}{B_{HA}}}$.Squaring both sides, $4 = \frac{32 \times 10^{-6}}{B_{HA}}$.Therefore, $B_{HA} = \frac{32 \times 10^{-6}}{4} = 8 \times 10^{-6} \,T$.

Class 12 Physics Magnetism and Matter Magnetic Equipment's (Tangent galvanometer, Vibration magnetometer and Neutral point)

Medium

$A$ vibration magnetometer is used at two different places $A$ and $B$ on the earth. The time period of a magnet suspended freely in the magnetometer at $A$ is twice that at $B$. If the horizontal component of the earth's magnetic field at $B$ is $32 \times 10^{-6} \,T$, then its value at $A$ is

AP EAMCET 2022 All AP EAMCET

A
$H_{A}=8 \times 10^{-6} \,T$
B
$H_{A}=32 \times 10^{-6} \,T$
C
$H_{A}=4 \times 10^{-6} \,T$
D
$H_{A}=16 \times 10^{-6} \,T$

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Magnetism and Matter

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Magnetic Equipment's (Tangent galvanometer, Vibration magnetometer and Neutral point)

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MediumAP EAMCET 2004

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$A$ bar-magnet of moment of inertia $49 \times 10^{-2} \,kg-m^2$ vibrates in a magnetic field of induction $0.5 \times 10^{-4} \,T$. The time period of vibration is $8.8 \,s$. The magnetic moment of the bar magnet is (in $\,A-m^2$)

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$A$ vibration magnetometer is used at two different places $A$ and $B$ on the earth. The time period of a magnet suspended freely in the magnetometer at $A$ is twice that at $B$. If the horizontal component of the earth's magnetic field at $B$ is $32 \times 10^{-6} \,T$, then its value at $A$ is

Similar Questions

$A$ bar magnet of moment of inertia $49 \times 10^{-2} \,kg-m^2$ vibrates in a magnetic field of induction $0.5 \times 10^{-4} \,T$. The time period of vibration is $8.8 \,s$. The magnetic moment of the bar magnet is (in $\,A-m^2$)

$A$ magnet is suspended horizontally in the Earth's magnetic field. When it is made to oscillate in a horizontal plane,its time period is $T$. If a wooden block of the same moment of inertia as the magnet is attached to it,what will be the new time period of the system?

$A$ bar-magnet of moment of inertia $49 \times 10^{-2} \,kg-m^2$ vibrates in a magnetic field of induction $0.5 \times 10^{-4} \,T$. The time period of vibration is $8.8 \,s$. The magnetic moment of the bar magnet is (in $\,A-m^2$)

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