Question

An equilateral triangle frame PQR of mass M and side a is kept under the influence of magnetic force due to inward perpendicular magnetic field B and gravitational field as shown in the figure.The magnitude and direction of current in the frame so that the frame remains at rest is

• A. $I=\frac{2Mg}{aB};anticlockwise$
• B. $I=\frac{2Mg}{aB};clockwise$
• C. $I=\frac{Mg}{aB};anticlockwise$
• D. $I=\frac{Mg}{aB};clockwise$

Answer 1

Answer: (B)

$I=\frac{2Mg}{aB};clockwise$

$\overrightarrow{F_{MNPQ}}=\overrightarrow{F_{MQ}}$ and this force should be upwards to balance the weight.

$\therefore ilB=mg$, where

$l=MQ=\frac{a}{2}$

$\therefore i\left(a/2\right)B=mg$ or $i=\frac{2Mg}{aB}$

Force is upwards if current is clockwise or current in MQ is towards right.