Question

In a magnetism experiment, the value of $\frac{m}{B}$ is measured using the deflection magnetometer. What should be the value of deflection lf the percentage error is minimum?

• A. ${30}^o$
• B. ${75}^o$
• C. ${45}^o$
• D. ${50}^o$

Answer 1

The correct option is C ${45}^o$

We have the formula for calculating, $\frac{m}{B}=\frac{4\pi }{{\mu }_o}\frac{(d^2-l^2{)}^2}{2d}\tan \theta$

= $k\tan \theta$

where $k=\frac{4\pi }{{\mu }_o}\frac{(d^2-l^2{)}^2}{2d}$

$\delta \left(\frac{m}{B}\right)=k{\sec }^2\theta \delta \theta$

% error in $\left(\frac{m}{B}\right)=\frac{\delta \left(\frac{m}{B}\right)}{\left(\frac{m}{B}\right)}=\frac{k{\sec }^2\theta \delta \theta }{k\tan \theta }\times 100$

$\frac{\delta \theta }{\sin \theta \cos \theta }\times 100=\frac{200\delta \theta }{\sin 2\theta }$

% error is minimum when sin 2 $\theta$ is maximum which is equal to 1.

$\therefore 2\theta ={90}^{\circ }\therefore \theta ={45}^{\circ }$