Question

A conductor PQRSTU, each side of length L, bent as shown in the figure, carries a current i and is placed in a uniform magnetic induction B directed parallel to the positive Y-axis. The force experience by the wire and its direction are

• A. 2iBL directed along the negative Z-axis
• B. 5iBL directed along the positive Z-axis
• C. iBL direction along the positive Z-axis
• D. 2iBL directed along the positive Z-axis

Answer 1

The correct option is C iBL direction along the positive Z-axis

As PQ and UT are collinear to B, therefore $F_{PQ}=F_{UT}=0$.
The current in TS and RQ are in mutually opposite direction. Hence,
$F_{TS}+F_{RQ}=0$, therefore, the force will act only on the segment SR whose value is Bil and its direction is +z.
Alternate method :
The given shape of the wire can be replaced by a straight wire of length l between P and U as shown below.
Hence, force on replaced wire PU will be F=Bil
and according to FLHR it is directed towards +z-axis.