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Electrostatics is the branch of physics that studies electric charges at rest. The fundamental concept involves understanding how charges interact and create electric fields. Imagine you have static charges, and they are not moving. These charges can exert forces on each other. This is electrostatics.
A conducting sphere helps in illustrating electrostatics. When a sphere is charged, the excess electric charge resides on the surface. This happens because like charges repel each other and seek to maximize their distance from each other. As a result, the charges spread uniformly over the conducting surface.
Additionally, the electrostatic potential at any point on the surface of a conducting sphere is the same. This is a crucial point because it simplifies calculations related to potential and electric fields. Understanding electrostatics helps us delve into related concepts like electric fields, Gauss's law, and potential differences.

The relationship between potential and charge is fundamental in electrostatics. For a conducting sphere, the electrostatic potential (V) at its surface due to a charge (Q) is given by:
\[ V = \frac{Q}{4 \pi \varepsilon_0 R} \]
Here, R is the radius of the sphere, and \( \varepsilon_0 \) is the permittivity of free space (鈦燶[ \varepsilon_0 = 8.85 \times 10^{-12} \mathrm{~F/m} \]).
To find the charge Q, we rearrange the equation:
\[ Q = V \times 4 \pi \varepsilon_0 R \]
Substitute the given values (V = 200 V, R = 0.15 m) to calculate the charge on the sphere:
\[ Q = 200 \times 4 \pi \times 8.85 \times 10^{-12} \times 0.15 \approx 3.337 \times 10^{-9} \mathrm{~C} \]
This equation shows us how the charge on a conducting sphere depends on its potential and radius. It also highlights how increasing either the radius or the potential will result in a higher charge.

The charge density on a conducting sphere is the amount of charge per unit area. To find it, first calculate the surface area (A) of the sphere using the formula:
\[ A = 4 \pi R^2 \]
For a sphere with radius (R) of 0.15 meters:
\[ A = 4 \pi (0.15)^2 \approx 0.2827 \mathrm{~m^2} \]
Next, you find the charge density (\( \sigma \)) by dividing the charge (Q) by the surface area (A):
\[ \sigma = \frac{Q}{A} \]
Substitute the values we calculated earlier:
\[ \sigma = \frac{3.337 \times 10^{-9} \mathrm{~C}}{0.2827 \mathrm{~m^2}} \approx 1.181 \times 10^{-8} \mathrm{~C/m^2} \]
This value represents how much charge is present per square meter on the surface of the sphere. Understanding this calculation is important in fields like material science and electronics, where charge distribution affects the behavior of materials and devices.