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    Please help me solve this question as i am very poor at lenz's law and using faraday's right hand or left hand rule.(I always get confused on which rule to use when)
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    this has nothing to do with faradays's LHR (which is to find the direction of the force on a current) and I doubt you need to know his RHR.

    When a current flows in a coil which end becomes north (flux leaving) and which becomes south (flux coming in)? You can tell this form the direction of the current. If you look at the end of the coil and the current is going round clockwise then this end is a south. Anticlockwise its a north.

    To induce and e.m.f. you need 3 things
    a) a B field,
    b) a conductor and
    c) relative movement (a changing field will do).

    Faradays law says that the magitude of the emf (V) is proportional to how quickly the flux lines are cut as the conductor/field moves or changes. As the switch is closed in the first question the field in the first coil grows from nothing to a steady state. As it changes an emf is induced in the secondary, as the 3 required things are there. As the secondary coil has a complete circuit then a current is also induced.
    This pulse of current in the secondary coil will produce a B field also, which, from lenz's law, will oppose the change in flux. The field produced by the secondary will be in the opposite direction to the field produced by the primary. It will only be there, however, while the field in the primary is growing. When the current/field in the primary has reached a steady state then there will no longer be an e.m.f. /current induced in the secondary and therefore no field will be produced by the secondary.

    Lenz's law is actually just conservation of energy. The induced e.m.f. must oppose the change in flux producing it. Imagine pushing a magnet into a coil attached to a bulb and making the bulb flash. The energy to light the bulb must be coming from your muscles i.e. you must be doing work, i.e. the field induced in the coil is opposing you pushing the magnet in. If the induced field "pulled" the magnet in AND the bulb flashed you would be getting energy for nothing.
    have a look at
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