Physics Derivations: Detailed Derivation of Physics Formulas

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Jasmine Grover

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Derivations in Physics are important to understand the concepts in a clear manner. It helps us understand how the important Physics formulas are derived. Physics Derivations help us identify the logic behind the concepts of Physics to enhance their application. The derivations in physics for the formulas are derived from experiments and observations. Questions on derivations are mostly asked in CBSE Board Examinations as well as entrance exams. We can find a logical connection between the phenomenon and its mathematical description through derivations. The important derivations include concepts from Electrostatics, Current Electricity, Optics, Motion, etc. Some of the important derivations in physics are given in this article along with examples to understand their application.


Derivation of Physics

Some of the important physics derivations are as follows – 


Physics Derivations – Some Important Concepts

Some of the important concepts of derivations of physics are as follows –  

  • Archimedes Principle

Archimedes Principle states that when we submerge an object in water, either partially or fully, the object will experience an upward buoyant force which is equal to the weight of the water that is displaced by the submerged object. 

  • Banking of Roads

Banking of Roads refers to when the edges of a curved road are raised a bit above the inner edge in a manner that the required centripetal force for the vehicles to take a safe turn is applied. This is to avoid skidding off a road. The edges are horizontally inclined to lift the outer edge of the road.  

  • Bragg’s Law

Bragg’s law is a special case of Laue diffraction that is known to be the determinant of angles that give out coherent and incoherent scattering from a crystal lattice. 

  • Maxwell Equations

Maxwell’s equations use a combination of Ampere’s Law of Current in a Conductor, Gauss’s Law of Electricity, Gauss’s Law of Magnetism, and Faraday’s Law of Electromagnetic Induction. It can be inferred from the equation that in an electromagnetic wave, the magnetic field and the electric field are perpendicular to each other as well as to the direction of propagation.

  • Mirror Formula

Mirror Formula refers to an equation that is derived that relates the image distance and the object distance with the focal length. A plane mirror is a kind of flat surface that produces a straight image wherein the back and the front of a real object is reversed.

  • Centripetal Acceleration

Centripetal acceleration is the force that acts on a body that is moving in a uniform circular motion. This centripetal force is perpendicular to the velocity in a circular motion. In addition to this, if the particles that are in a circular motion reduce or increase their speeds, then acceleration is generated, which further causes the net acceleration to vary.


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CBSE CLASS XII Related Questions

  • 1.

    A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is (i) $\sqrt{2}$, and (ii) $\sqrt{3}$.


      • 2.
        Two point charges -Q and Q are located at points (d, 0) and (0, d) respectively, in x-y plane. The electric field E at the origin will be:

          • \(\frac{1}{4\pi\epsilon_0} \frac{\sqrt{2}Q}{d^2} (\hat{i} - \hat{j})\)
          • \(\frac{1}{4\pi\epsilon_0} \frac{\sqrt{2}Q}{d^2} (-\hat{i} - \hat{j})\)
          • \(\frac{1}{4\pi\epsilon_0} \frac{Q}{d^2} (\hat{i} - \hat{j})\)
          • \(\frac{1}{4\pi\epsilon_0} \frac{Q}{d^2} (-\hat{i} - \hat{j})\)

        • 3.

          A rectangular loop of size 5 cm $\times$ 8 cm is lying in the $x$-$y$ plane in a uniform magnetic field $\vec{B} = (2.0\ \text{T})\hat{k}$. The total magnetic flux linked with the loop is:

            • 80 Wb
            • 16 Wb
            • \(8 \times 10^{-2}\) Wb
            • \(8 \times 10^{-3}\) Wb

          • 4.

            Find the ratio $\dfrac{\lambda_\alpha}{\lambda_p}$ of the de Broglie wavelength $\lambda_\alpha$ associated with an alpha particle to the de Broglie wavelength $\lambda_p$ associated with a proton if both are moving with the same velocity.


              • 5.

                Consider a cylindrical conductor of length $l$ and area of cross-section $A$. Current $I$ is maintained in the conductor and electrons drift with velocity $\vec{v}_d$ ($|\vec{v}_d| = \frac{e|\vec{E}|}{m}\tau$), (where symbols have their usual meanings). Show that the conductivity $\sigma$ of the material of the conductor is given by

                $$\sigma = \frac{ne^2}{m}\tau.$$


                  • 6.

                    A circular coil of 100 turns and radius $\left(\frac{10}{\sqrt{\pi}}\right)$ cm carrying current of $5.0\,\text{A}$ is suspended vertically in a uniform horizontal magnetic field of $2.0\,\text{T}$. The field makes an angle $30^\circ$ with the normal to the coil. Calculate:

                    (I) the magnetic dipole moment of the coil, and

                    (II) the magnitude of the counter torque that must be applied to prevent the coil from turning.

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