Question

A current-carrying, straight wire is kept along the axis of a circular loop carrying a current. This straight wire

Options

• will exert an inward force on the circular loop

•  will exert an outward force on the circular loop

• will not exert any force on the circular loop

• will exert a force on the circular loop parallel to itself.

Answer 1

will not exert any force on the circular loop 

The magnetic force on a wire carrying an electric current i is given as​  \[\vec{F} = i . ( \vec{l} \times \vec{B} )\] , where l is the length of the wire and B is the magnetic field acting on it. If a current-carrying straight wire is kept along the axis of a circular loop carrying current, then according to the right-hand thumb rule, the magnetic field due to the wire on the current-carrying loop will be along its circumference, which contains a current element \[i d \vec{l}\] .

So, the cross product will be​

\[( \vec{l}  \times  \vec{B} ) = 0\] 

\[ \Rightarrow  \vec{F}  = 0\]

Thus, the straight wire will not exert any force on the loop.