Question

A wire, bent in the form of a right-angled triangle $ABC$ carries a current of $1\text{A}$. It is placed in the region of a uniform magnetic field $B=0.2\text{T}$ as shown in the figure. If $AC=1\text{m}$, the net force on the wire is -

• A. $1\text{N}$
• B. $3\text{N}$
• C. $2\text{N}$
• D. $0\text{N}$

Answer 1

The correct option is D $0\text{N}$

If the current carrying conductor in the form of a loop of any arbitrary shape is placed in a uniform magnetic field, the force on the loop is,

$\overrightarrow{F}=\oint I\overrightarrow{dl}\times \overrightarrow{B}=\oint I\left(dl\right)B\sin \theta \hat{\eta }$

$=IB\sin \theta \oint dl\hat{\eta }$

For a closed loop, $\oint dl=0$

$\therefore \overrightarrow{F}=0$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, option $\left(D\right)$ is the correct answer.

Why this Question? This question gives you an understanding of the concept of force on a conducting loop placed in a uniform magnetic field.