Modulus of Elasticity is the measure of the stiffness of a material. It quantifies the relationship between stress (force per unit area) and strain (deformation) in a material. The modulus of elasticity is also known as Young's modulus or the elastic modulus.

Definition:
The modulus of elasticity is defined as the ratio of stress to strain within the elastic limit of a material. It represents the intensity of stress required to produce a unit strain in the material.

Explanation:
When a material is subjected to a tensile or compressive force, it deforms and changes its shape. The modulus of elasticity provides a measure of how much the material will deform under a given stress.

For example, consider a metal wire. When a force is applied to the wire, it will stretch or compress depending on the direction of the force. The modulus of elasticity determines the extent to which the wire will deform. A material with a high modulus of elasticity will undergo minimal deformation under the applied stress, while a material with a low modulus of elasticity will experience significant deformation.

Mathematical Representation:
Mathematically, the modulus of elasticity (E) is calculated by dividing the stress (σ) by the strain (ε):

E = σ / ε

Where:
E = Modulus of elasticity (Young's modulus)
σ = Stress (force per unit area)
ε = Strain (deformation)

Units:
The modulus of elasticity is usually expressed in pascals (Pa) or megapascals (MPa).

Importance:
The modulus of elasticity is an important property of materials used in engineering and construction. It helps determine the ability of a material to withstand stress and maintain its shape without permanent deformation. Materials with high moduli of elasticity, such as steel, are preferred for structural components as they can withstand large loads and resist deformation. On the other hand, materials with low moduli of elasticity, such as rubber, are used in applications that require flexibility and elasticity.

Conclusion:
The modulus of elasticity is a fundamental property of materials that relates stress to strain. It provides a measure of the stiffness or rigidity of a material and helps determine its behavior under applied forces.