# Induced emf in a solenoid from a current carrying wire nearby

#### silentstorm

Say I have a solenoid that has a magnetic field Bo Sin(ωt) passing through its axis. What will be the EMF induced in the solenoid as a result ? I know it'll be a function of Cos (ωt) but I am more interested in how my choice of the solenoid will affect the EMF that I'll ultimately measure.

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#### Hassan2

Calculate the fields separately and supperpose them. If the solenoid axis is paralel to z-axis, you can calculate the field for the wire first and add the solenoid field to its z-component.

#### silentstorm

Hassan, thanks for the response, but I dont understand what you mean. There is only one field here which is an external magnetic field. If you put a solenoid into a magnetic field, I am guessing the size (Radius) of the solenoid would affect the induced EMF ? I am interested in knowing what that relation would be.

#### Hassan2

Hassan, thanks for the response, but I dont understand what you mean. There is only one field here which is an external magnetic field. If you put a solenoid into a magnetic field, I am guessing the size (Radius) of the solenoid would affect the induced EMF ? I am interested in knowing what that relation would be.

Yes you are right. If it had no effect, the emf would be independant of the solenoid current. So by choosing a low resistance parallel with the slenoid we would get very high power from a fixed input power!

The effect is infact what we know as the inductace of the solenoid.
In order to calculate the current and emf when you have current in the coil, just imagine a voltage source in series with the inductance and the load. Calculation beomes simple then.

Added: The interaction is so that by increasing the solenoid current, the flux passing though it decrease and this results a lowe emf.

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