Question

Consider the inferences given below in respect of the following current loop of wire kept in a magnetic field $\vec{B}$.

1. The magnitude and direction of force on the element $AC$ of the wire is $\frac{\sqrt{3}}{2}ILB$ directed into the page.
2. The magnitude and direction of force on the element $AB$ of the wire is $\frac{\sqrt{3}}{2}ILB$ directed into the page.
3. The total force on the loop $ABCA$ is zero.
Which of the above is/are not true?

• A. 1 and 2
• B. 2 only
• C. 1 and 3
• D. 2 and 3

Answer 1

Answer: (B)

Force on the element $AC$ of the wire is
$F_{AC}=I\left(L\cos 30^{\circ }\right)B\sin 90^{\circ }=\frac{\sqrt{3}}{2}ILB$
It is directed into the page.
$\therefore$ Statement 1 is true.
Force on the element $AB$ of the wire is
$F_{AB}=ILB\sin \left(90^{\circ }-30^{\circ }\right)=ILB\sin 60^{\circ }=\frac{\sqrt{3}}{2}ILB$
It is directed out of the page.
$\therefore$ Statement 2 is not true.
Total force on the current carrying loop in a uniform magnetic field is zero.
$\therefore$ Total force on the loop $ABCD$ is zero.
Statement 3 is true.