Question 189: Magnetism and Matter

Question

A wire carrying current I is bent in the shape
ABCDEFA as shown, where rectangle ABCDA
and ADEFA are perpendicular to each other. If
the sides of the rectangles are of lengths a and
b, then the magnitude and direction of
magnetic moment of the loop ABCDEFA is
![](https://imagex.cdn.examgoal.net/jgy2xukexwhla1/cedbb5a8-d217-4b48-870c-ea9aaa761b0b/c660ce90-f3fd-11ea-8293-3b6cc591631c/file-jgy2xukexwhla2-454w.png)

Accepted Answer

For ABCD
${\overrightarrow M _1}$ = abI$\widehat k$
For DEFA
${\overrightarrow M _2}$ = abI$\widehat j$
$\overrightarrow M  = {\overrightarrow M _1} + {\overrightarrow M _2}$
= $abI\left( {\widehat k + \widehat j} \right)$
= $abI\sqrt 2 \left( {{{\widehat k} \over {\sqrt 2 }} + {{\widehat j} \over {\sqrt 2 }}} \right)$

Answer

$\sqrt 2 $abI, along $\left( {{{\widehat j} \over {\sqrt 5 }} + {{2\widehat k} \over {\sqrt 5 }}} \right)$

Answer

abI, along $\left( {{{\widehat j} \over {\sqrt 5 }} + {{2\widehat k} \over {\sqrt 5 }}} \right)$

Answer

$\sqrt 2 $abI, along $\left( {{{\widehat j} \over {\sqrt 2 }} + {{\widehat k} \over {\sqrt 2 }}} \right)$

Answer

abI, along $\left( {{{\widehat j} \over {\sqrt 2 }} + {{\widehat k} \over {\sqrt 2 }}} \right)$

Magnetism and Matter

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is

Choose the correct answer: