Given below are two statements:
Statement I : Electromagnetic waves are not deflected by electric and magnetic field.
Statement II : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as `E_0= sqrt(mu_0/varepsilon_0)B_0`.
In the light of the above statements,choose the correct answer from the options

Options

A. Statement I is true but statement II is false
B. Statement I is false but statement II is true
C. Both statement I and Statement II are true
D. Both statement I and Statement II are true

Answer

To solve the question, we need to analyze the two statements provided:

**Statement I:** Electromagnetic waves are not deflected by electric and magnetic fields.

**Statement II:** The amplitude of the electric field and the magnetic field in electromagnetic waves are related to each other as \( E_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}} B_0 \).

### Step 1: Analyze Statement I
Electromagnetic waves, such as light, are transverse waves consisting of oscillating electric and magnetic fields. These waves propagate through space and are not affected by static electric or magnetic fields. This is because electromagnetic waves are not charged particles; they do not have a net charge that would cause them to be deflected by electric or magnetic fields.

**Conclusion for Statement I:** True.

### Step 2: Analyze Statement II
The relationship between the electric field \( E_0 \) and the magnetic field \( B_0 \) in electromagnetic waves is given by the equation:

\[ c = \frac{E_0}{B_0} \]

where \( c \) is the speed of light in a vacuum. This can also be expressed using the permeability \( \mu_0 \) and permittivity \( \varepsilon_0 \) of free space as:

\[ c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \]

From this, we can derive the relationship between \( E_0 \) and \( B_0 \):

\[ E_0 = c B_0 = \frac{B_0}{\sqrt{\mu_0 \varepsilon_0}} \]

This means that the given expression \( E_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}} B_0 \) is incorrect. The correct relationship should involve \( c \) as shown above.

**Conclusion for Statement II:** False.

### Final Conclusion
- Statement I is True.
- Statement II is False.

Thus, the correct answer is that Statement I is true and Statement II is false.