A tangent galvanometer is used for detection and measurement...

A tangent galvanometer is used for detection and measurement of low electric currents. It is based on tangent law in magnetism, according to which $F=G \tan \theta$, where $\theta$ is angle with $H$ made by a magnet suspended freely under the combined effect of $H$ and $(F \perp H) .$ Now, $F=\frac{\mu_{0}}{4 \pi} \frac{2 \pi n I}{r}$, where $n$ is number of turns in the coil of radius, $r$ earrying current $I$. From, $F=H \tan \theta$, we get $$ I=\frac{2 r H}{\mu_{0} n} \tan \theta=K \tan \theta $$ where $K$ is called reduction factor of tangent galvanometer. Value of $H$ on earth's surface is (a) $0.32 \mathrm{G}$ (b) $0.32 \mathrm{~T}$ (c) $0.32 \times 10^{-4} \mathrm{G}$ (d) $0.32 \times 10^{-5} \mathrm{~T}$

A tangent galvanometer is used for detection and measurement of low electric currents. It is based on tangent law in magnetism, according to which $F=G \tan \theta$, where $\theta$ is angle with $H$ made by a magnet suspended freely under the combined effect of $H$ and $(F \perp H) .$ Now, $F=\frac{\mu_{0}}{4 \pi} \frac{2 \pi n I}{r}$, where $n$ is number of turns in the coil of radius, $r$ earrying current $I$. From, $F=H \tan \theta$, we get $$ I=\frac{2 r H}{\mu_{0} n} \tan \theta=K \tan \theta $$ where $K$ is called reduction factor of tangent galvanometer.
Value of $H$ on earth's surface is
(a) $0.32 \mathrm{G}$
(b) $0.32 \mathrm{~T}$
(c) $0.32 \times 10^{-4} \mathrm{G}$
(d) $0.32 \times 10^{-5} \mathrm{~T}$

Key Concepts

Magnetic Field Intensity (H)

This is a measure of the strength and direction of a magnetic field at a specific location. In geophysics, the value of H on the Earth’s surface indicates the intensity of the terrestrial magnetic field, which can vary with location and altitude. It is a critical parameter in understanding magnetic interactions and in designing instruments such as galvanometers.

Gauss and Tesla Units

These are the units used to quantify magnetic field strength. One Tesla is equal to 10,000 Gauss. Understanding the conversion between these units is important when comparing measurements, especially since the Earth’s magnetic field is typically expressed in Gauss, while many scientific instruments and formulas use Tesla.

Tangent Law in Magnetism

The tangent law relates the horizontal components of magnetic fields acting on a magnetic needle. It states that the tangent of the angle of deflection of the needle is proportional to the ratio of the magnetic field produced by a current-carrying coil to the ambient magnetic field. This principle is foundational for the operation of tangent galvanometers.

Tangent Galvanometer

A tangent galvanometer is an instrument used to measure low currents by utilizing the tangent law. It consists of a coil through which current flows, creating a magnetic field perpendicular to the Earth’s magnetic field, causing a magnetized needle to deflect. The angle of deflection, which follows the tangent law, is then used to quantify the current.

Reduction Factor (K)

The reduction factor is a constant derived from the coil’s geometry and the ambient magnetic field strength, linking the tangent of the deflection angle to the current flowing through the coil. It simplifies the calculation and calibration of the tangent galvanometer, making it easier to determine the current from the observed deflection.

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