Question

A wire $\text{abcdef}$ with each side of length $l$ is bent as shown in figure. It carries a current $I$. It is placed in a uniform magnetic field $B$ parallel to y direction. what is the magnetic force experienced by wire ?

• A. $2BIl$, along $+y$ direction
• B. $BIl$, along $-x$ direction
• C. $2BIl$, along $-x$ direction
• D. $BIl$ , along $-y$ direction

Answer 1

The correct option is B $BIl$, along $-x$ direction

For the given wire $\text{abcdef}$, the effective length vector will be in a direction connecting the initial point $\text{a}$ and final point $\text{f}$ on the wire.


$\overrightarrow{L}=l\widehat{\left(k\right)}$
$\overrightarrow{B}=B\hat{j}$

Thus, magnetic force on the wire is given by,

${\overrightarrow{F}}_m=I(\overrightarrow{L}\times \overrightarrow{B})$

${\overrightarrow{F}}_m=I(l\widehat{\left(k\right)}\times B\hat{j})$

$\overrightarrow{F_m}=BIl\widehat{-i}$

Thus, magnetic force is $BIl$ along $-x$ direction

why this question ? It uniquely tests your visualization of effective length vector for an arbitrary shaped wire placed in a three-dimensional orientation.