Question

A circular coil of radius 20 cm and 20 turns of wire is mounted vertically with its plane in magnetic. meridian. A small magnetic needle (free to rotate about vertical axis) is placed at the center of the coil. It is deflected through ${45}^o$ when a current is passed through the coil and in equilibrium (Horizontal component of earth's field is $0.34\times {10}^{-4}T$). The current in coil is :

• A. $\frac{17}{10\pi }A$
• B. $6A$
• C. $6\times {10}^{-3}A$
• D. $\frac{3}{50}A$

Answer 1

The correct option is A $\frac{17}{10\pi }A$

The arrangement is a tangent galvanometer

$I=Ktan\theta$

$=\frac{2r{B}_H}{{\mu }_{0}n}tan\theta$

$\therefore I=\frac{2\ast 20\ast {10}^{-2}\ast 0.34\ast {10}^{-9}}{4\pi \ast {10}^{-7}\ast 20}\ast tan{45}^{\circ }$

$=\frac{2\ast 3.4}{4\pi }=\frac{17}{10\pi }ampere$