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. In the use of tangent galvanometer, $H$ is (a) earth's magnetic ficld (b) horizontal component of earth's magnetic field (c) vertical component of earth's magnetic ficld (d) None of the above

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.
In the use of tangent galvanometer, $H$ is
(a) earth's magnetic ficld
(b) horizontal component of earth's magnetic field
(c) vertical component of earth's magnetic ficld
(d) None of the above

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Key Concepts

Tangent Law

The tangent law in magnetism establishes that the ratio of the magnetic field produced by a current-carrying coil to an external magnetic field is equal to the tangent of the angle of deflection of a magnetic needle. This law is central to understanding how devices like the tangent galvanometer measure current by observing angular deflections.

Reduction Factor

The reduction factor is a constant specific to the design of a tangent galvanometer that relates the measured deflection angle to the actual current flowing through the device. It takes into account factors like coil geometry and the magnetic field strength, allowing for direct computation of current from the observed angle.

Earth's Magnetic Field (Horizontal Component)

In the context of a tangent galvanometer, the relevant magnetic field is the horizontal component of Earth’s magnetic field. This component interacts with the magnetic field produced by the current to determine the deflection of the needle, making it a crucial element in the device's operation and current measurement.

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