In a particular region of space, the magnetic and electric fields have energy densities of 0.2 J/m3 and 4

J/m3 , respectively. Calculate the strength of the magnetic and electric fields in this region.

To calculate the strength of the magnetic and electric fields in this region, we need to use the equations that relate energy density to field strength.

For the magnetic field (B), the energy density (u) is given by:

u = (1/2) * μ0 * B^2

where μ0 is the vacuum permeability, which is a constant equal to 4π × 10⁻⁷ T m/A.

Rearranging this equation, we can solve for B:

B = √ (2u / μ0)

Now, let's plug in the values. The energy density for the magnetic field is 0.2 J/m³, so:

B = √ (2 * 0.2 J/m³ / (4π × 10⁻⁷ T m/A)

Simplifying this equation will give us the strength of the magnetic field.

Similarly, for the electric field (E), the energy density (u) is given by:

u = ε0 * E^2 / 2

where ε0 is the vacuum permittivity, which is a constant equal to 8.85 × 10⁻¹² C²/N m².

Rearranging this equation, we can solve for E:

E = √ (2u / ε0)

Now, let's plug in the values. The energy density for the electric field is 4 J/m³, so:

E = √ (2 * 4 J/m³ / (8.85 × 10⁻¹² C²/N m²)

Simplifying this equation will give us the strength of the electric field.