(C) For a short bar magnet in $\tan A$ position,the magnetic field $B$ is given by $B = \frac{\mu_0}{4\pi} \frac{2M}{d^3}$.In a deflection galvanomete

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$\tan^{-1}\left(\frac{\sqrt{3}}{8}\right)$

(C) For a short bar magnet in $\tan A$ position,the magnetic field $B$ is given by $B = \frac{\mu_0}{4\pi} \frac{2M}{d^3}$.In a deflection galvanometer,$B = H \tan \theta$,where $H$ is the horizontal component of Earth's magnetic field.Thus,$\frac{\mu_0}{4\pi} \frac{2M}{d^3} = H \tan \theta$ ..... $(i)$When the distance is doubled $(d' = 2d)$,the new deflection $\theta'$ is given by:$\frac{\mu_0}{4\pi} \frac{2M}{(2d)^3} = H \tan \theta'$ ..... $(ii)$Dividing equation $(ii)$ by $(i)$:$\frac{\tan \theta'}{\tan \theta} = \frac{1}{2^3} = \frac{1}{8}$$\tan \theta' = \frac{\tan 60^\circ}{8} = \frac{\sqrt{3}}{8}$$\theta' = \tan^{-1}\left(\frac{\sqrt{3}}{8}\right)$

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

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The needle of a deflection galvanometer shows a deflection of $60^\circ$ due to a short bar magnet at a certain distance in $\tan A$ position. If the distance is doubled,the deflection is

A
$\sin^{-1}\left(\frac{\sqrt{3}}{8}\right)$
B
$\cos^{-1}\left(\frac{\sqrt{3}}{8}\right)$
C
$\tan^{-1}\left(\frac{\sqrt{3}}{8}\right)$
D
$\cot^{-1}\left(\frac{\sqrt{3}}{8}\right)$

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Magnetism and Matter

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

$A$ current-carrying coil is placed with its axis perpendicular to the $N-S$ direction. Let the horizontal component of the Earth's magnetic field be $H_0$ and the magnetic field inside the loop be $H$. If a magnet is suspended inside the loop,it makes an angle $\theta$ with $H$. Then $\theta =$

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$A$ very small magnet is placed in the magnetic meridian with its south pole pointing north. The null point is obtained $20 \, cm$ away from the centre of the magnet. If the earth's magnetic field (horizontal component) at this point is $0.3 \, gauss$,the magnetic moment of the magnet is:

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The magnetic moments of two bar magnets of same size are in the ratio $1:2$. When they are placed one over the other with their similar poles together,their period of oscillation in a magnetic field is $3 \, s$. If one of the magnets is reversed,then the period of oscillation in the same field will be ......... $s$.

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$A$ tangent galvanometer shows a deflection of $45^{\circ}$ when a $10 \, mA$ current passes through it. If the horizontal component of the Earth's magnetic field is $3.6 \times 10^{-5} \, T$ and the radius of the coil is $10 \, cm$,find the number of turns in the coil.

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$A$ magnetic needle has a magnetic moment of $5 \times 10^{-2} \text{ A m}^2$ and a moment of inertia of $8 \times 10^{-6} \text{ kg m}^2$. It has a period of oscillation of $2 \text{ s}$ in a magnetic field $\vec{B}$. The magnitude of the magnetic field is approximately:

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The needle of a deflection galvanometer shows a deflection of $60^\circ$ due to a short bar magnet at a certain distance in $\tan A$ position. If the distance is doubled,the deflection is

Similar Questions

$A$ current-carrying coil is placed with its axis perpendicular to the $N-S$ direction. Let the horizontal component of the Earth's magnetic field be $H_0$ and the magnetic field inside the loop be $H$. If a magnet is suspended inside the loop,it makes an angle $\theta$ with $H$. Then $\theta =$

$A$ very small magnet is placed in the magnetic meridian with its south pole pointing north. The null point is obtained $20 \, cm$ away from the centre of the magnet. If the earth's magnetic field (horizontal component) at this point is $0.3 \, gauss$,the magnetic moment of the magnet is:

$A$ tangent galvanometer shows a deflection of $45^{\circ}$ when a $10 \, mA$ current passes through it. If the horizontal component of the Earth's magnetic field is $3.6 \times 10^{-5} \, T$ and the radius of the coil is $10 \, cm$,find the number of turns in the coil.

$A$ magnetic needle has a magnetic moment of $5 \times 10^{-2} \text{ A m}^2$ and a moment of inertia of $8 \times 10^{-6} \text{ kg m}^2$. It has a period of oscillation of $2 \text{ s}$ in a magnetic field $\vec{B}$. The magnitude of the magnetic field is approximately:

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