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

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: