Total Charge in a Dielectric Sphere
To find the total charge inside a dielectric sphere with a uniform charge distribution, we start with the concept of charge density and the relationship between charge, volume, and dielectric properties.
Charge Density
- The total charge \( Q \) is uniformly distributed over the volume of the sphere.
- The volume \( V \) of the sphere can be calculated using the formula:
\[
V = \frac{4}{3} \pi a^3
\]
- The charge density \( \rho \) is given by:
\[
\rho = \frac{Q}{V} = \frac{Q}{\frac{4}{3} \pi a^3}
\]
Dielectric Constant
- The dielectric constant \( \varepsilon_R \) indicates how a material responds to an electric field.
- In this case, \( \varepsilon_R = 2 \) suggests that the dielectric material can store electric energy differently compared to vacuum.
Conclusion on Total Charge Inside
- It is essential to note that the dielectric constant does not affect the actual total charge \( Q \) present within the sphere.
- Therefore, regardless of the dielectric properties, the total charge inside the dielectric sphere remains \( Q \).
Total Charge Calculation
- The total charge inside the dielectric sphere is simply \( Q \), as the charge is uniformly distributed throughout the volume.
Final Statement
- Thus, the total charge inside the dielectric sphere of radius \( a \) with a dielectric constant \( \varepsilon_R = 2 \) is \( Q \). The dielectric properties influence the electric field and polarization but not the total charge contained within the volume.