Physics
Physics
Problem
A solid plastic sphere initially carries a uniform positive charge density throughout its volume. A small, completely empty spherical cavity is drilled out of the interior without removing any charge from the remaining material. Qualitatively describe the electric field that now exists inside the cavity and state the reason for its presence.Intuitive explanation
The key insight is that the field inside the cavity comes from superposition: treat the charged sphere-with-cavity as a complete charged sphere minus a sphere of charge at the cavity's location. Since the field inside a uniformly charged sphere varies linearly with position, removing that "negative sphere" leaves behind a uniform field throughout the cavity—pointing away from the cavity's center toward the center of the original sphere. This uniform field is the signature of superposition at work.
Intuitive explanation
The key insight is that the field inside the cavity comes from superposition: treat the charged sphere-with-cavity as a complete charged sphere minus a sphere of charge at the cavity's location. Since the field inside a uniformly charged sphere varies linearly with position, removing that "negative sphere" leaves behind a uniform field throughout the cavity—pointing away from the cavity's center toward the center of the original sphere. This uniform field is the signature of superposition at work.