Question

An equilateral triangular frame ABC of mass M and side L is at rest under influence of horizontal magnetic field $B_0$ and gravitational field as shown in figure, then

• A. Minimum current required in frame for equilibrium is $\frac{\sqrt{3}Mg}{LB}$.
• B. Minimum current required in frame for equilibrium is $\frac{Mg}{LB}$.
• C. Direction of current must be from A to B.
• D. If frame is displaced slightly in vertical direction, it oscillates.

Answer 1

Answer: (A), (C), (D)

The correct options are
A Minimum current required in frame for equilibrium is $\frac{\sqrt{3}Mg}{LB}$.
C Direction of current must be from A to B.
D If frame is displaced slightly in vertical direction, it oscillates.

By force equilibrium
$Mg=i{L}_{eff}{B}_0$
$L_{eff}=l_{pq}=\frac{L}{\sqrt{3}}$
$Mg=i\frac{L}{\sqrt{3}}B\Rightarrow i=\frac{\sqrt{3}Mg}{LB}$
$\overrightarrow{F_B}=i\overrightarrow{l}\times \overrightarrow{B}$ so direction of i is from A to B.
As frame displaces down, $l_{eff}$ increases. So $F_B$ increases and restores frame, so motion is oscillatory.