how can the magnetic field produced around a current carrying conductor be detected
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If we bring a magnetic needle or a compass near a current carrying conductor and if the needle of the compass deflects then we can detect magnetic field around a current carrying conductor.
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Force on a current carrying conductor in a magnetic field and Fleming's left hand rule. An electric current flowing through a conductor produces a magnetic field, this field exerts a force on a magnet placed near the conductor the direction of this force is found out by Fleming's left hand rule.
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