A Spherical Capacitor Conundrum?

📌 CONCEPT: The electrostatic potential difference between two points in a region with varying charge distribution can be found using the relationship between electric field and potential difference.

📐 RULE / FORMULA: The potential difference (V) between two points in a spherical region with charge Q and radius r is given by V = kQ/r, where k is Coulomb's constant.

💡 WORKED EXAMPLE: To find the potential difference in the 10-15 cm region, we first find the potential difference between the 10 cm and 20 cm radii due to the 6 μC charge. Using V = kQ/r, we find that V1 = k*6 μC/20 cm. Next, we find the potential difference between the 10 cm and 15 cm radii due to the 6 μC charge. Using V = kQ/r, we find that V2 = k*6 μC/15 cm. The potential difference in the 10-15 cm region is V2 - V1.

⚠️ COMMON MISTAKE: Students often forget to consider the charge distribution and the geometry of the system, assuming that the potential difference remains constant throughout the region.