In the context of electrostatics, when you mention an "inner sphere" being "earthed," it typically refers to a situation involving a conducting sphere that is connected to the Earth (grounded). Let's break down what this means:
Conducting Sphere: A conducting sphere is a spherical object made of a material that allows electric charges to move freely within it. Conductors, such as metals, have electrons that can easily move throughout the material. This is in contrast to insulators, which do not allow the easy flow of electric charges.
Earthed (Grounded): When a conducting object is "earthed" or "grounded," it means that it is connected to the Earth, which serves as a massive reservoir of charge with an effectively infinite capacity to absorb or provide electrons. Grounding a conductor involves connecting it to the Earth through a conductive pathway, such as a metal wire buried in the ground.
Electrostatics: Electrostatics deals with stationary electric charges and their interactions. When charges are at rest, they create electric fields that influence other charges in their vicinity.
Now, let's consider the scenario you described: an "inner sphere" that is earthed. Here's how it might play out:
Suppose you have a setup with two concentric conducting spheres, where one sphere is inside the other. The inner sphere is connected to the Earth (grounded), while the outer sphere is not. Let's say the inner sphere carries a net charge.
What happens in this scenario is that the net charge on the inner sphere will distribute itself in such a way that it's evenly distributed across the outer surface of the inner sphere. This is due to the repulsion of like charges and the tendency of charges to move freely within a conductor.
Since the inner sphere is earthed, any excess charge it carries will flow into the Earth, effectively neutralizing the inner sphere's charge. This happens because the Earth can supply or absorb an unlimited amount of charge due to its vast size and capacity for electrons.
The outer sphere, which is not earthed, will remain unaffected by the inner sphere's charge redistribution since there is no pathway for charges to flow to or from the Earth.
In summary, when an inner conducting sphere is earthed (grounded), any excess charge it carries will distribute itself on its outer surface, and the sphere's overall charge will be neutralized as charges flow into the Earth. This principle is based on the properties of conductors, the behavior of electric charges, and the concept of grounding in electrostatics.