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JEE Main 2026 Preparation: Question Papers, Solutions, Mock Tests & Strategy Unacademy » JEE Study Material » Physics » Dimensional Formula of Intensity

Dimensional Formula of Intensity

Power in a unit area is called intensity. The study of the relationship between physical quantities is known as dimensional analysis.

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The dimensions of a physical quantity are the powers to which the basic quantities are elevated to represent that amount. The dimensional formula of any physical quantity is an equation that explains how and which of the base quantities are contained in that amount. It is written by enclosing the symbols representing base amounts in square brackets with the corresponding power, i.e. [].

E.g., the dimension formula of displacement is [L].

In general, the total height of a wave is called its amplitude. According to Physics, Amplitude refers to the maximum dispersion of a point on a vibrating subject from its equilibrium point. As a result, the amplitude of a pendulum is one-half of the distance travelled by the bob as it moves from one side to the other. Vibrating sources produce waves, and their amplitude is proportional to the source’s amplitude.

Intensity

Power in a unit area is called intensity. Its unit is kg.s-³. In the case of light, intensity is defined as the rate at which light spreads over a surface of a given area. Its magnitude generally depends upon the amplitude and wave under propagation. Sound intensity is sometimes known as acoustic intensity.

Mathematically, it is represented by the following formula:

hh3

Unit of intensity is watt per square metre.

We can classify intensity into two types: low intensity and high intensity. 

Some examples of intensity are the intensity of the kinetic energy carried by drops of water from a sprinkler, the ability to run miles on end at a good speed, and the quickness with which a treadmill is moving.

We know that intensity can be defined as power in a unit area, so we can also define intensity as energy density per unit volume multiplied by the velocity at which the energy is moving. It is measured on the plane perpendicular to the direction of energy propagation.

We can compare the intensity of one sound with another if the frequency of both sounds is the same. If the ratio of power values is 10, then the difference of the sounds is measured as 1 bel.

Dimensional formula of intensity

hh4

The intensity of the magnetising field

A part of the magnetic field that arises from the external current rather than the intrinsic properties is magnetic field intensity or magnetic field strength, or magnetic intensity. Also, the magnetic field is the area around the magnet or where the magnetism effect is felt. In a wire that carries current, the formation of magnetic fields takes place. The direction of induced current and the direction of the magnetic field is directly related to each. 

In the simplest form, magnetism can be defined as a type of interaction that occurs among the moving charged particles. Spatially separate objects and materials are related to magnetic interactions transmitted by magnetic fields of magnets. A magnetic field is a unique form of electromagnetism.

Conclusion

Intensity is nothing but power in a unit area. We can also define intensity as energy density per unit volume multiplied by the velocity at which the energy is moving. It is measured on the plane perpendicular to the direction of energy propagation. Its unit is kg.s-3. Its magnitude generally depends upon the amplitude and wave under propagation. Some examples of intensity are the kinetic energy carried by drops of water from a sprinkler, the ability to run miles on end at a good speed, and the quickness with which a treadmill is moving.

faq

Frequently asked questions

Get answers to the most common queries related to the IIT JEE Examination Preparation.

What is the formula of intensity?

Ans. Intensity is defined as the product of energy density and wave speed. In the case of light, intensity i...Read full

What is the SI unit of intensity?

Ans. The SI unit of intensity is given as ...Read full

Write some of the examples of intensity.

Ans. Following are some of the examples of intensity: ...Read full

How can we define 1 bel?

Ans. We can compare the intensity of one sound with another if the frequency of both sounds is the same. If ...Read full

Find the power of a wave whose intensity is given as 20×10-5 watt per square metre. Area of cross section is 50 m2.

Ans. Intensity = 20 ×10-5...Read full

Ans. Intensity is defined as the product of energy density and wave speed. In the case of light, intensity is defined as the rate at which light spreads over a surface of a given area. Sound intensity is sometimes known as acoustic intensity.

Ans. The SI unit of intensity is given as

Ans. Following are some of the examples of intensity:

  • The intensity of the kinetic energy carried by drops of water from a sprinkler
  • The ability to run miles on end at a good speed
  • The quickness with which a treadmill is moving.
  • The sound of our blood pulsing through our ears at night.
  • The sound of a leaf falling to the ground.

Ans. We can compare the intensity of one sound with another if the frequency of both sounds is the same. If the ratio of power values is 10, then the difference of the sounds is measured as 1 bel.

Ans. Intensity = 20 ×10-5 W/m2

Area = 50 m2

Intensity = Power = Intensity × Area

Power = 20 ×10-5 × 50 W

  = 10-2 W

Ans. The dimensional formula depicts the dependency of physical quantity with fundamental physical quantity, along with the powers.

Example: Speed = Distance / Time

The distance can be written in length [L]

Time can be written as [T]

The dimensional formula would be [ M0 L1 T-1]

Hence, we can conclude that the speed is dependent on only length and time, not mass.

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