SCALAR MAGNITUDE: WHAT IT CONSISTS OF, CHARACTERISTICS AND EXAMPLES - PHYSICAL - 2025

A scalar quantity is a numerical quantity whose determination only requires the knowledge of its value with respect to a certain unit of measure of its same kind. Some examples of scalar quantities are distance, time, mass, energy, and electric charge.

Scalar quantities are generally represented by a letter or by the absolute value symbol, for example A or ǀ A ǀ. The magnitude of a vector is a scalar magnitude and can be obtained mathematically by algebraic methods.

Likewise, scalar quantities are represented graphically with a straight line of a certain length, without a specific direction, related to a scale factor.

What is a scalar quantity?

In Physics, a scalar quantity is a physical quantity represented by a fixed numerical value and a standard unit of measurement, which does not depend on the reference system. Physical quantities are mathematical values ​​related to measurable physical properties of a physical object or system.

For example, if you want to obtain the speed of a vehicle, in km / h, you just need to divide the distance traveled by the time elapsed. Both quantities are numerical values ​​accompanied by a unit, therefore speed is a scalar physical quantity. A scalar physical quantity is the numerical value of a measurable physical property without a specific orientation or sense.

Not all physical quantities are scalar quantities, some are expressed by means of a vector that has numerical value, direction and sense. For example, if you want to obtain the speed of the vehicle, you must determine the movements made during the elapsed time.

These movements are characterized by having a numerical value, a direction and a specific sense. Consequently the speed of the vehicle is a vector physical quantity as is the displacement.

Characteristics of a scalar quantity

-It is described with a numerical value.

-Operations with scalar magnitudes are governed by basic algebraic methods such as addition, subtraction, multiplication and division.

-The variation of a scalar magnitude only depends on the change in its numerical value.

-It is represented graphically with a segment that has a specific value associated with a measurement scale.

-The scalar field allows determining the numerical value of a scalar physical quantity at each point in physical space.

Scalar product

The scalar product is the product of two vector quantities multiplied by the cosine of the angle θ that they form with each other. When the scalar product of two vectors is calculated, the result that is obtained is a scalar quantity.

The scalar product of two vector quantities a and b is :

ab = ǀaǀǀbǀ. cosθ = ab.cos θ

a = is the absolute value of vector a

b = absolute value of vector b

Product of two vectors. By Svjo (https://commons.wikimedia.org/wiki/File:Scalar-dot-product-1.png)

Scalar field

A scalar field is defined by associating a scalar magnitude at each point in space or region. In other words, the scalar field is a function that shows a position for each scalar quantity within space.

Some examples of a scalar field are: the temperature at each point on the Earth's surface at an instant of time, the topographic map, the pressure field of a gas, the charge density and the electric potential. When the scalar field does not depend on time it is called stationary field

When representing graphically the set of points of the field that have the same scalar magnitude equipotential surfaces are formed. For example, the equipotential surfaces of point electric charges are concentric spherical surfaces centered in the charge. When an electric charge moves around the surface the electric potential is constant at every point on the surface.

Scalar field of pressure measurements.

Examples of scalar quantities

Here are some examples of scalar quantities that are physical properties of nature.

Temperature

It is the average kinetic energy of the particles in an object. It is measured with a thermometer and the values ​​obtained in the measurement are scalar quantities associated with how hot or how cold an object is.

Mass

To obtain the mass of a body or object, it is necessary to count how many particles, atoms, molecules it has, or to measure how much material the object makes up. A mass value can be obtained by weighing the object with a balance and you do not need to set the orientation of the body to measure its mass.

Weather

Scalar magnitudes are mostly related to time. For example the measure of years, months, weeks, days, hours, minutes, seconds, milliseconds, and microseconds. Time has no direction or sense of direction.

Volume

It is associated with the three-dimensional space that a body or substance occupies. It can be measured in liters, milliliters, cubic centimeters, cubic decimeters among other units and it is a scalar quantity.

Speed

The measurement of the speed of an object in kilometers per hour is a scalar quantity, it is only required to establish the numerical value of the object's path as a function of the elapsed time.

Electric charge

The protons and neutrons of subatomic particles have an electrical charge that is manifested by the electrical force of attraction and repulsion. Atoms in their neutral state have zero electric charge, that is, they have the same numerical value of protons as neutrons.

Energy

Energy is a measure that characterizes the ability of a body to perform work. By the first principle of Thermodynamics it is established that the energy in the universe remains constant, it is not created or destroyed, it is only transformed into other forms of energy.

Electric potential

The electric potential at any point in space is the electric potential energy per unit charge, it is represented by equipotential surfaces. The potential energy and the electric charge are scalar quantities, therefore the electric potential is a scalar quantity and depends on the value of the charge and the electric field.

Density

It is the measure of the amount of mass of a body, particles or substances in a certain space and is expressed in units of mass per units of volume. The numerical value of the density is obtained, mathematically, dividing the mass by the volume.

References

1. Spiegel, MR, Lipschutz, S and Spellman, D. Vector Analysis. sl: Mc Graw Hill, 2009.
2. Muvdi, BB, Al-Khafaji, AW and Mc Nabb, J W. Statics for Engineers. VA: Springer, 1996.
3. Brand, L. Vector Analysis. New York: Dover Publications, 2006.
4. Griffiths, D J. Introduction to Electrodynamics. New Jersey: Prentice Hall, 1999. pp. 1-10.
5. Tallack, J C. Introduction to Vector Analysis. Cambridge: Cambridge University Press, 2009.