At room temperature, if the relative permittivity of water...

At room temperature, if the relative permittivity of water is 80 and the relative permeability be $0.0222$ then the velocity of light in water is $\mathrm{m} / \mathrm{s}$
(A) $2.5 \times 10^{8}$
(B) $2.26 \times 10^{8}$
(C) $3.5 \times 10^{8}$
(D) $3 \times 10^{8}$

Key Concepts

Speed of Light in Vacuum

The speed of light in vacuum, denoted as c, is a fundamental constant in physics, approximately equal to 3 × 10^8 m/s. It serves as a benchmark for calculating the speed of light in other media when modified by the medium's relative permittivity and permeability.

Electromagnetic Wave Propagation in Materials

When electromagnetic waves travel through a medium other than vacuum, their speed is modified by the medium's relative permittivity and relative permeability. The relationship is given by c_medium = c / ?(?r·?r), where c is the speed of light in vacuum. This formula encapsulates how the electric and magnetic properties of the medium determine the phase velocity of the wave.

Relative Permittivity

Relative permittivity, often denoted as ?r, measures how much a material can ‘permit’ electric field lines compared to vacuum. It indicates the extent to which a material can be polarized by an external electric field, affecting the propagation of electromagnetic waves through the medium by altering the capacitance and energy storage within the material.

Relative Permeability

Relative permeability, denoted as ?r, quantifies how a material responds to a magnetic field compared to vacuum. It describes the degree to which a material can be magnetized, influencing the magnetic component of electromagnetic wave propagation in the medium.

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