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 $\frac{\sqrt{3}}{2} I L B$ directed into the page.
2. The magnitude and direction of force on the element $A B$ of the wire is $\frac{\sqrt{3}}{2} I L B$ directed into the page.
3. The total force on the loop $A B C A$ 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
$F_{A C}=I\left(L \cos 30^{\circ}\right) B \sin 90^{\circ}=\frac{\sqrt{3}}{2} I L B$
It is directed into the page.
$\therefore $ Statement 1 is true.
Force on the element $A B$ of the wire is
$F_{A B}=I L B \sin \left(90^{\circ}-30^{\circ}\right)=I L B \sin 60^{\circ}=\frac{\sqrt{3}}{2} I L B$
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 $A B C D$ is zero.
Statement 3 is true.