Question

The radius of each coil of a Helmholtz galvanometer is $0.1m$ and number of turns in each is $25$. When a current is passed in it then the deflection of magnetic needle observed as ${45}^o$. If the horizontal component of earth's magnetic field is $0.314\times {10}^{-4}T$ then the value of current will be

• A. $0.14A$
• B. $0.28A$
• C. $0.42A$
• D. $0.07A$

Answer 1

The correct option is A $0.14A$

$\text{By Tangent Law:}B=B_H\tan \theta$

$\text{For Helmholtz galvanometer}B=\frac{8{\mu }_{0}NI}{5\sqrt{5}R}$

$\frac{8{\mu }_{0}NI}{5\sqrt{5}R}=B_H\tan \theta$

$\text{Here,}\theta ={45}^o,B_H=0.314\times {10}^{-4}\text{T},R=0.1\text{m},N=25$

$\therefore \frac{8\times 4\pi \times {10}^{-7}\times 25I}{5\sqrt{5}\times 0.1}=0.314\times {10}^{-4}\tan {45}^o$

$\Rightarrow I=\frac{5\sqrt{5}\times 0.1\times 0.314\times {10}^{-4}\tan {45}^o}{8\times 4\pi \times {10}^{-7}\times 25}$

$\Rightarrow I=0.14\text{A}$