How the solenoid gets the linear motion when the current is passed in the coil?

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Solenoids function as switches in pneumatic controllers by using an energized coil to create a magnetic field. This magnetic field generates a force that moves a ferromagnetic rod into the coil. If the rod is a permanent magnet, reversing the current changes the poles of the electromagnet, allowing the rod to be pushed out in the opposite direction. The operation of solenoids can be explained using Fleming's Left Hand Rule, which relates to the direction of force in magnetic fields. Understanding these principles is crucial for effectively utilizing solenoids in various applications.
Raj
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The Solenoids which are used for pneumatic controller uses the solenoid as a switch to control the value opening and closing. This is done by passing current to through the coil which produces the magnetic field . But i would like to know how the generated magnetic field will move the solenoid rod?
 

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When the coil is energized, a magnetic field is created. This field produces a force that acts on the ferromagnetic rod and moves it into the coil up to a certain allowed point. If the rod is a permanent magnet reversing the current direction in the coil reverses poles of the electromagnet and produced force can be in oposite direction to push out the rod.
 
Is it based on Flemings Left hand rule ?
 
Right hand rule of a screw thread. I think that's the name
 
I am trying to understand how transferring electric from the powerplant to my house is more effective using high voltage. The suggested explanation that the current is equal to the power supply divided by the voltage, and hence higher voltage leads to lower current and as a result to a lower power loss on the conductives is very confusing me. I know that the current is determined by the voltage and the resistance, and not by a power capability - which defines a limit to the allowable...

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