Consider the inferences given below in respect of the following current loop of wire kept is a magnetic field $\vec B$
$A.$ The force on the element $AC$ of the wire is $\frac{{\sqrt 3 }}{2}\,ILB$ directed into the page
$B.$ The force on the element $AB$ of the wire is $\frac{{\sqrt 3 }}{2}\,ILB$ directed into the page
$C.$ The total force on the loop $ABCA$ is zero.
Which of the above is /are not true ?
Diffcult
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By right hand plam rule
direction of $\vec {\mathrm{F}}_{\mathrm{m}}$ is inward for $\mathrm{AC}$ $\&$ outward
for $\mathrm{AB}$
Now
$\mathrm{F}_{\mathrm{CB}}=\mathrm{BI} \frac{\mathrm{L}}{2}\left(\sin 180^{\circ}\right)=0$
$\mathrm{F}_{\mathrm{AC}}=\frac{\mathrm{BIL} \sqrt{3}}{2} \otimes$
$\vec{\mathrm{F}}_{\mathrm{AB}}+\vec{\mathrm{F}}_{\mathrm{AC}}+\vec{\mathrm{F}}_{\mathrm{CB}}=0$
$\Rightarrow \quad \vec{\mathrm{F}}_{\mathrm{AB}}=-\vec{\mathrm{F}}_{\mathrm{AC}} \Rightarrow \quad \vec{\mathrm{F}}_{\mathrm{AB}}=\frac{\sqrt{3} \mathrm{BI}\mathrm{L}}{2} \odot$
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