Examples of physical quantities: energy, heat, work, force, speed, acceleration, electric currents, gravitational field strength, electric field strength, inductance, magnetic induction, electromagnetic induction, etc.
All these quantities are measurable and characterized by a certain numerical value that is multiple of the standard value chosen strictly by convention.
But there are some physical quantities that are characterized not only by the numerical value but also by the direction and purpose in acting.
Let’s take the Force as an example. It is not enough to say that a certain force is 5 N (Newton) but we have to know on which direction and sense it actions. The Force is a vector quantity. The force vector, as any other vector, has an application point (the point where it begins to act), a module (vector size characterized by the numerical value), a direction and a sense.
The Current Intensity is a Scalar Physical Quantity and it represents the number of electrons which cross the conductor section in a unit of time. Do not understand that the electrons leave the power plant for a walk to get to our house. Electrons oscillate, electric field propagate (300.000 km/s) and electric energy is transported through waves.
Electrical power is equal to voltage multiplied with the intensity of electric power. As power is greater, the energy carried is higher. To increase the power, we need to increase either the intensity or tension. To increase the intensity, we should increase the thickness of the conductor, which is inconvenient and requires more material. The voltage can be increase with the help of transformers.
The intensity of the electric current is a scalar quantity but it can’t be said the same about the intensity of the electric field which is a vector quantity. Intensity of any physical field is a vector quantity.
If we read the definition of any intensity of any field it starts something like this: “Intensity of … field is the force that …” so, …IS THE FORCE. The force is a vector quantity and acceleration is also a vector quantity.
Mechanical work is a scalar physical quantity, although it is equal with the increment of force and motion, force is a vector physical quantity (scalar product of a vector and a scalar is commutative and also a vector). There is no contradiction here because the sense of force is meaningless; the same amount of mechanical work is obtained. The only thing that matters is just the direction of force. If it is perpendicular to the direction then it does not perform mechanical work.
There are some physical quantities that sometimes are scalar and sometimes are vector such as length or area. Many machines and equipment have the sense of electromagnetic force depending on the direction of motion of a conductor placed in the magnetic field of an electromagnet or the sense of rotation of a surface of a condenser plate.
To know in advance which will be the sense of the electromagnetic force, the left hand’s rule and Fleming rule has been introduced. I have simplified I much as I could.