2010 AIPMT-PRE Moving Charges and MagnetismForce on a Current-carrying Conductor in a Magnetic Field Easy Question 6 of 7 in Force on a Current-carrying Conductor in a Magnetic Field

A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is $\vec{F}$, the net force on the remaining three arms of the loop is

A $\vec{F}$
B $3\vec{F}$
C $-\vec{F}$
D $-3\vec{F}$

The answer is C.

Solution

The net force on a closed current-carrying loop in a uniform magnetic field is zero: $\oint I\,d\vec{l}\times\vec{B} = I\left(\oint d\vec{l}\right)\times\vec{B} = 0$
Let $\vec{F}_1 = \vec{F}$ be the force on one arm and $\vec{F}_2$ the net force on the remaining three arms.
$\vec{F}_1 + \vec{F}_2 = 0$
$\vec{F}_2 = -\vec{F}_1 = -\vec{F}$

Concept Net force on a closed loop

Force on a Current-carrying Conductor in a Magnetic Field in past papers

7 questions from this chapter have appeared across 6 exam years.