(a) According to Lenz’s law, the end of the coil facing the S-pole of the magnet coil become S-pole so as to repel the approaching magnet. For this to happen, the current in the coil will flow in the direction QRPQ.
(b) For the coil on left: For the reason given in (a) the current in the left coil will flow in the direction PRQP.
For the coil on right: According to Lenz’s law, the end of the coil facing the N-pole of the magnet will become S-pole so as to attract the magnet moving away from it. For this to happen, the current in the coil will flow in the direction YZXY.
(c) When the tapping key is just closed, the current flow’s in the coil and hence magnetic flux linked with it starts growing. According to Lenz’s law, the induced current in the adjoining coil should set up in a direction so as to oppose the growth of magnetic flux linked with the coil. It will happen so, if the direction of magnetic field produced by the induced current in the adjoining coil is from right to left i.e. the induced current is produced in the direction YZX.
(d) Due to change in rheostat setting (resistance decreased), the current in the coil and hence magnetic flux linked with it, will start increasing. According to Lenz’s law, the induced current in the adjoining coil should set up in a direction. so as to oppose the increasing in magnetic flux linked with the coil. It will happen. So, if the direction of magnetic field produced by the induced current in the adjoining coil is from right to left i.e. the induced current is produced in the direction ZYX.
(e) Before releasing the tapping keg, the right end of the core is N-pole and the magnetic field linked with the coil is from left to right. As the tapping keg is released, the magnetic field linked with the coil will start collapsing. According to Lenz’s Law the induced current in the adjoining coil should set up in a direction so as to reinforce the collapsing magnetic field. It will happen so, if the direction of magnetic field produced by induced current in the adjoining coil is from left to right i.e. the induced current is produced in the direction XRY.
(f) The current flowing through the straight conductor produces magnetic field in the plane of the coil. Since no magnetic flux is linked with the coil, no induced current will be set up in the coil.