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Question
A straight wire carrying an electric current is placed along the axis of a uniformly charged ring. Will there be a magnetic force on the wire if the ring starts rotating about the wire? If yes, in which direction?
Solution
The magnetic force on a wire carrying an electric current i is \[\vec{F} = i . ( \vec{l} \times \vec{B} )\], where l is the length of the wire and B is the magnetic field acting on it. If a uniformly charged ring starts rotating around a straight wire, then according to the right-hand thumb rule, the magnetic field due to the ring on the current carrying straight wire placed at its axis will be parallel to it. So, the cross product will be
\[( \vec{l} \times \vec{B} ) = 0\]
\[ \Rightarrow \vec{F} = 0\]
Therefore, no magnetic force will act on the wire.
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