Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Electromagnetic waves carry energy but not momentum.
Reason (R): Mass of a photon is zero.
In the light of the above statements, choose the most appropriate answer from the options given below:
- Assertion (A) is true: Electromagnetic waves do indeed carry energy and momentum. The momentum of electromagnetic waves is related to their energy by \( p = \frac{E}{c} \), where \( c \) is the speed of light, and \( E \) is the energy of the wave.
- Reason (R) is also true: The mass of a photon is zero, but this does not imply that electromagnetic waves do not carry momentum. Photons carry momentum even though they have no rest mass. However, Reason (R) does not correctly explain Assertion (A), because the zero mass of photons does not prevent them from carrying momentum. Thus, the correct answer is (3).
A parallel plate capacitor has two parallel plates which are separated by an insulating medium like air, mica, etc. When the plates are connected to the terminals of a battery, they get equal and opposite charges, and an electric field is set up in between them. This electric field between the two plates depends upon the potential difference applied, the separation of the plates and nature of the medium between the plates.
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: