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The solenoid coil concentrates the magnetic field lines through the interior when the solenoid wire carries a current.

I am curious about a different case, however. If a (separate) straight wire went through the center of an unpowered solenoid coil, and this wire carried current, what would the induced effect be on the solenoid coil (say the solenoid is either grounded or left open)? Would any induced effect fight the current on the wire through the center?

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No, a wire fed axially through the centreline of a solenoid would not induce anything into the solenoid coil. The magnetic fields (if both are energized) will be at right angles. There would be no transformer action.

At much higher frequencies there will be circulating eddy currents induced in the solenoid winding (from the straight wire) but these won't be significant below tens or hundreds of kHz

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  • \$\begingroup\$ Could there be any parasitic capacitance effect? \$\endgroup\$ May 13, 2013 at 16:25
  • \$\begingroup\$ There will be capacitance between the straight wire and solenoid just like there is between the centre conductor of a coax cable and its shield \$\endgroup\$
    – Andy aka
    May 13, 2013 at 16:27
  • \$\begingroup\$ Would the induced eddy currents at the higher RF frequencies subtract from the overall current in the straight wire? \$\endgroup\$ May 13, 2013 at 16:27
  • \$\begingroup\$ The induced eddy currents will tend to reduce the inductance of the straight wire and cause a little more current to flow in it but for a "normal" solenoid wire it will be a small percentage. \$\endgroup\$
    – Andy aka
    May 13, 2013 at 16:29
  • \$\begingroup\$ @Andyaka: isnt' this how current-sensing transformers work? They are exactly an axial spool of wire with a single lead passed through the middle. \$\endgroup\$ Jun 24, 2013 at 21:28

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