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A solenoid is connected to a battery so ...

A solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, the current will

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When the iro core is inserted in the current carrying solenoid, the magnetic field increases due to the magnetisation of iron core and consequently the flux increases. According to Lenz's law, the emf produced must oppose this increases in flux, which can be done by making decrease in current. So, the current will decrease.
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