Question

A new system of unit is evolved in which the values of \(\mu_{0}\) and \(\varepsilon_{0}\) are 2 and 8 respectively. Then the speed of light in this system will be (A) \(0.25\) (B) \(0.5\) (C) \(0.75\) (D) 1

Short answer

The speed of light in the new system of units can be found using the formula \(c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\). Substituting the given values of \(\mu_0 = 2\) and \(\varepsilon_0 = 8\), we get \(c = \frac{1}{\sqrt{(2)(8)}} = \frac{1}{\sqrt{16}} = \frac{1}{4}\). The correct answer is (A) \(0.25\).

Step-by-step solution

Write down the formula for the speed of light in terms of permeability and permittivity constants

In this step, we will write down the formula relating the speed of light to the permeability and permittivity constants: \(c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\).

Substitute the given values

Now we will substitute the given values of \(\mu_0\) and \(\varepsilon_0\) into the formula: \(c = \frac{1}{\sqrt{(2)(8)}}\).

Calculate the speed of light

Let's simplify the expression to find the value of the speed of light: \(c = \frac{1}{\sqrt{16}} = \frac{1}{4}\).

Choose the correct answer from the options

Since the speed of light is \(\frac{1}{4}\), the correct answer is (A) \(0.25\).