Question

The certain amount of current when flowing in a properly set tangent galvanometer, produces a deflection of $45^{\circ} $ . The current be reduced by a factor of $ \sqrt{3} $ , the deflection would

• A. decrease by $30^{\circ} $
• B. decrease by $ 15^{\circ} $
• C. increase by $ 15^{\circ} $
• D. increase by $ 30^{\circ} $

Answer 1

The Correct Option is B

The correct answer is B:decrease by \(15\degree\)
When current is passed through tangent galvanometer, a magnetic field is created given by 
\(B=\frac{\mu_{0} n I}{2 r}\) 
When it is set in plane, then from tangent law, 
\(B=B_{H} \tan \theta\)
\(\Rightarrow \frac{\mu_{0} n I}{2 r}=B_{H} \tan \theta\)
\(\Rightarrow I=\left(\frac{2 r B_{H}}{\mu_{0} n}\right) \tan \theta\)
\(\Rightarrow \quad I=K \tan \theta\) 
where \(K\) is reduction factor. 
Given \(I_{2}=\frac{I_{1}}{\sqrt{3}}, \theta_{1}=45^{\circ}\)
\(\therefore \frac{I_{1}}{I_{1} / \sqrt{3}}=\frac{\tan 45^{\circ}}{\tan \theta_{2}}\)
\(\Rightarrow \tan \theta_{2}=\frac{1}{\sqrt{3}}\)
\(\Rightarrow \theta_{2}=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
\(=30^{\circ}\) 
Hence, deflection decreases by 
\(45^{\circ}-30^{\circ}=15^{\circ}\)