Question

A non-planar closed loop of arbitrary shape carrying a current $I$ is placed in uniform magnetic field.The force acting on the loop

• A. is zero only for one orientation of loop in magnetic field
• B. is zero for two symmetrically located positions of loop in magnetic field
• C. is zero for all orientations
• D. is never zero

Answer 1

Answer: (C)

is zero for all orientations

Magnetic force on current carrying wire $F=i[\overrightarrow{L}\times \overrightarrow{B}]$

Net force on a closed loop placed in uniform magnetic field is zero.

$\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}-\overrightarrow{D}=0$

OR $\overrightarrow{D}=\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}$

Closing side of the polygon in opposite flow represent the resultant vector.

The magnetic force on current carrying is given by $d\overrightarrow{F}=id\overrightarrow{l}\times \overrightarrow{B}$

This force when integrated over the loop, from property of vector sum, it comes as zero.