How will the capacitance change when 64 spherical conducters of equal ...
Introduction
When 64 spherical conductors of equal size, each with a capacitance "C", are joined together to form a larger spherical conductor, the overall capacitance changes significantly.
Capacitance of a Single Sphere
- The capacitance "C" of a single spherical conductor is defined as the ability to store charge per unit potential.
Combining Spheres
- When multiple spheres are combined, they effectively create a larger sphere.
- The new capacitance of the larger sphere can be derived from the properties of capacitors in parallel.
Capacitance in Parallel
- For capacitors in parallel, the total capacitance (C_total) is the sum of individual capacitances.
- Therefore, if each of the 64 spheres has a capacitance C, the total capacitance when combined is:
- C_total = 64 * C
Physical Interpretation
- When the smaller spheres unite, they maintain the same potential but can store more charge due to their increased surface area.
- This results in a larger effective capacitance.
Conclusion
- The formation of a larger spherical conductor from 64 smaller spheres increases the overall capacitance to 64 times the capacitance of an individual sphere.
- This principle illustrates how combining conductors enhances their ability to store electrical energy, which is vital in various applications in electrical engineering and physics.