Question

Figure shows an equilateral triangle $ABC$ of side $l$ carrying currents as shown, and placed in a uniform magnetic field $B$ perpendicular to the plane of triangle. The magnitude of magnetic force on the triangle is

• A. $ilB$
• B. $3ilB$
• C. $2ilB$
• D. $zero$

Answer 1

Answer: (A)

$ilB$

Equating the incoming current to outgoing current at each of the nodes $A,B$ and $C$, one gets the current in sides $AB,BC$ and $CA$.
Force on side $AB,F_{AB}=ilB$
Sum of forces on sides $BC$ and $CA$ is equivalent to force on side $BA$ carrying current $2i$.
Force on side $AB,F_{BA}=2ilB$
$F_{AB}$ and $F_{BA}$ are opposite to each other. Hence, net force is $ilB$.