Question

A current of 10 A is flowing in a wire of length 1.5 m. When it is placed in a uniform magnetic field of 2 Tesla then a force of 15 N acts on it. The angle between the magnetic field and the direction of current flow will be :

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is A ${30}^o$

Force on the current carrying wire:
$\overrightarrow{F}=\int i(\overrightarrow{dl}\times \overrightarrow{B})$
$\therefore 15=10\times 1.5\times 2\sin \theta$ where $\theta$ is the angle between $\overrightarrow{dl}$ and $\overrightarrow{r}$
$\Rightarrow \sin \theta =\frac{15}{10\times 1.5\times 2}0.5$
$\Rightarrow \theta ={30}^0$