A tangent galvanometer has a coil of 25 turns and a radius of 15 cm. The horizontal component o

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A tangent galvanometer has a coil of 25 turns and a radius...

A tangent galvanometer has a coil of 25 turns and a radius of $15 \mathrm{~cm}$. The horizontal component of the earth's magnetic field is $3 \times 10^{-5} \mathrm{~T}$. The current required to produce a deflection of $45^{\circ}$ in it is (a) $0.29 \mathrm{~A}$ (b) $0.14 \mathrm{~A}$ (c) $1.2 \overline{\mathrm{A}}$ (d) $3.6 \times 10^{-5} \mathrm{~A}$

A tangent galvanometer has a coil of 25 turns and a radius of $15 \mathrm{~cm}$. The horizontal component of the earth's magnetic field is $3 \times 10^{-5} \mathrm{~T}$. The current required to produce a deflection of $45^{\circ}$ in it is
(a) $0.29 \mathrm{~A}$
(b) $0.14 \mathrm{~A}$
(c) $1.2 \overline{\mathrm{A}}$
(d) $3.6 \times 10^{-5} \mathrm{~A}$

Key Concepts

Earth's Magnetic Field (Horizontal Component)

The horizontal component of Earth's magnetic field is the part of the planet's overall magnetic field that runs parallel to the Earth's surface. It serves as the reference field in tangent galvanometers against which the field generated by the coil is compared, allowing for the determination of the current based on the measured deflection.

Tangent Galvanometer

A tangent galvanometer is an instrument used to measure electric current by using the deflection of a magnetic needle. Its operation is based on balancing the magnetic field created by a current-carrying coil against the horizontal component of the Earth's magnetic field, resulting in a deflection that follows the tangent law.

Magnetic Field due to a Circular Current Loop

The magnetic field at the center of a circular current loop is calculated using principles from the Biot-Savart law. The field depends on factors such as the number of turns in the coil, the current passing through it, and the radius of the loop, and is given by the formula involving these quantities alongside the magnetic constant.

Tangent Law

The tangent law is used in the operation of a tangent galvanometer and relates the tangent of the deflection angle of a magnetic needle to the ratio of the magnetic field produced by the current-carrying coil to the horizontal component of the Earth's magnetic field. This law is key to translating a measured deflection into a value for the current.

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