Electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius 10cm surrounding the total charge is 25 V-m. The flux over a concentric sphere of radius 20cm will be

To determine the electric flux through a concentric sphere of radius 20 cm, we can use Gauss's Law, which states that the electric flux through a closed surface is directly proportional to the total charge enclosed within that surface. The law is mathematically expressed as:

Gauss's Law

Mathematically, Gauss's Law is represented as:

Φ = Q_enc / ε₀

Where:

• Φ is the electric flux through the closed surface.
• Q_enc is the total charge enclosed by the surface.
• ε₀ is the permittivity of free space, approximately equal to 8.85 x 10^-12 C²/(N·m²).

Understanding the Given Information

In your scenario, we know that the electric flux through a spherical surface of radius 10 cm is 25 V·m. This value represents the total electric flux due to the charge enclosed within that sphere. Since the charge distribution is static and the charge remains the same, the total charge enclosed will also be the same for any concentric spherical surface surrounding it.

Applying Gauss's Law

Since the charge enclosed does not change as we move to a larger sphere (in this case, the 20 cm radius sphere), the electric flux through the 20 cm sphere will also be the same as that through the 10 cm sphere. Thus, we can conclude:

Electric Flux through the 20 cm sphere = Electric Flux through the 10 cm sphere

Therefore, the electric flux through the concentric sphere of radius 20 cm is also 25 V·m.

Visualizing the Concept

Think of it this way: if you have a balloon filled with air, the amount of air inside the balloon represents the charge. Whether the balloon is small or inflated to a larger size, the total amount of air (or charge) inside remains constant. Consequently, the pressure (or electric flux) exerted on the surface of the balloon will be the same regardless of its size, as long as the amount of air remains unchanged.

Final Thoughts

In summary, because the total charge remains constant regardless of the radius of the spherical surface, the electric flux through both the 10 cm and 20 cm spheres is identical. Thus, the answer is:

Electric Flux through the 20 cm sphere = 25 V·m