The region around a magnet within which its influence can be experienced is called magnetic field.

NS - permanent magnet
ABCD - coil wire
B₁ B₂ - carbon brushes
S₁ S₂ - split ring

The number of magnetic field lines crossing unit area kept normal to the direction of field lines is called magnetic flux density. Its unit is Wb/m².

No, if two magnetic lines of force intersect then there will be two tangents and hence two directions of the magnetic field at the point of intersection. This is not possible.

First law: Whenever there is a change in magnetic flux linked with a coil, an electric current is induced. The induced potential difference lasts so long as there is a change in the magnetic flux linked with the coil.
Second law: The magnitude of the induced current is directly proportional to the rate of change of magnetic flux linked with the coil

(i) The cost of generation of AC is less than the cost of generation of DC.
(ii) AC can be easily converted into D.C.
(iii) Only alternating voltage can be stepped up or stepped down by using a transformer.
(iv) AC can be transmitted to distant places without much loss of electric power than DC.

Depending upon the number of turns in the primary and secondary coils, we can step-up or step-down the voltage in the secondary coil.

Step up transformer: The transformer used to change a low alternative voltage to a high alternating voltage is called a step up transformer. ie (V_s>V_p ). In a step up transformer, the number of turns in the secondary coil is more than the number of turns in the primary coil (N_s > N_p). 
Step down transformer: The transformer used to change a high alternating voltage to a low alternating voltage is called a step down transformer (V_s < V_p). In a step down transformer, the number of turns in the secondary coils are less than the number of turns in the primary coil (N_s N_p).

Principle: An electric motor works on the principle that a current carrying conductor placed in a magnetic field experiences a force. The direction of force is given by Fleming's left hand rule.
Construction: An electric motor consists of the following main parts.
Armature: It is a rectangular coil ABCD having a large number of turns of this insulated copper wire wound over a soft iron core. The armature is placed between the poles of the field magnet and it can be rotated about an axis perpendicular to the magnetic field lines.
Split rings (commutators ): It consists of a cylindrical metal ring split into two halves S1 & S2. As the coil rotates, the split rings also rotate about the same axis of rotation. The function of the split ring is to reverse the direction of current in the coil after every half rotation. Carbon brushes: Two graphite or flexible metal rods maintain a sliding contact with split rings S1 and S2 alternately.
Battery: A battery of few cells is connected to the brushes. The current from the battery flows to the armature coil through the brushes and the split rings with split rings S1 and S2 alternately battery flows to the armature coil through the brushes and the split rings.
Working: A simple coil is placed inside two poles of a magnet. Now look at the current carrying conductor segment AB. The direction of the current is towards B, whereas in the conductor segment CD the direction is opposite. As the current is flowing in opposite directions in the segments AB and CD, the direction of the motion of the segments would be in opposite directions according to Fleming's left hand rule. When two ends of the coil experience force in opposite direction, they rotate. If the current flow is along the line ABCD, then the coil will rotate in clockwise direction first and then in anticlockwise direction. If we want to make the coil rotate in anyone direction, say clockwise, then the direction of the current should be along ABCD in the first half of the rotation and along DCBA in the second half of the rotation. When the gap in the split ring commutator is aligned with terminals X and Y there is no flow of current in the coil. But, as the coil is moving, it continues to move forward bringing one of the split ring commutator in contact with the carbon brushes X and Y. The reversing of the current is repeated at each half rotation, giving rise to a continuous rotation of the coil.