(a)
The length of the given coil is
Magnetic field strength,
Resistance of the loop is
The velocity at which the rod is moved is given as
The formula to calculate the induced emf is,
Substitute values in the above formula.
The Lenz’s law determines the polarity of the induced emf. The induced emf must oppose the cause of the change. With reference to the Fleming’s right hand rule, the induced current should flow from P to Q, so the end P shows positive polarity and Q shows negative polarity.
(b)
When key K is open, charge is developed at the ends of the rods and on closing the key, this charge flows in the form of current.
Therefore, yes, the excess charge is maintained due to continuous flow of the current in the circuit on closing key K.
(c)
When the rod starts to move in the magnetic field, excess change is developed at the ends of the rod which develops an electric force. This force cancels the magnetic force on the electron, thus the net force on the electrons is zero.
(d)
The formula to calculate the force on the conductor moving in magnetic field is,
Where,
Induced current is calculated as,
The length of the rod is
Magnetic field strength,
Substitute the value in the above formula,
Thus, the retarding force on the rod is
(e)
The power from external source is required to overcome the resisting force of
The velocity at which the rod moves is given as
The power is calculated as,
When key K is open, there is no current flow in the rod, thus no power is required.
(f)
The formula to calculate the power, in terms of current
Thus, the power dissipated as heat is
(g)
If the magnetic field is parallel to the rod, then there will not be any induced emf as the coil would not cut any flux, moving in the parallel direction.
Thus, the induced emf in the coil will be zero.