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

Answer: (C)

Ibl direction along the positive Z-axis

Answer 2

As PQ and UT are parallel to Q, therefore $F _ { P Q } = F _ { U T } = 0$

The current in TS and RQ are in mutually opposite direction. Hence, $F _ { T S } - F _ { R Q } = 0$

Therefore the force will act only on the segment SR whose value is Bil and it’s 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

and according to FLHR it is directed towards +z-axis