To determine the net force on the point charge \( q \) placed inside one of the spherical shells, we need to consider the properties of electric fields generated by charged objects, particularly nonconducting shells. Let's break this down step by step.
Understanding the Setup
We have two spherical shells, each with a uniformly distributed positive charge \( Q \) and radius \( d \). They are positioned 10d apart. A positive point charge \( q \) is located inside one of these shells, specifically at a distance \( d/2 \) from the center of that shell. The key point here is that the shells are nonconducting and very thin.
Electric Field Inside a Charged Shell
According to Gauss's law, the electric field inside a uniformly charged spherical shell is zero. This means that any point inside the shell experiences no net electric field due to the shell itself. Therefore, the electric field generated by the shell containing charge \( Q \) does not exert any force on the charge \( q \) located inside it.
Effect of the Other Shell
Now, let’s consider the second shell, which is located 10d away from the first shell. Since the charge \( q \) is inside the first shell, it does not interact with the second shell directly through electric fields. The electric field outside a uniformly charged shell behaves as if all the charge were concentrated at the center of the shell. However, since \( q \) is inside the first shell, it does not feel any force from the second shell either.
Calculating the Net Force
Given that the electric field inside the first shell is zero and the second shell does not exert any force on the charge \( q \), we can conclude that:
- The electric field due to the first shell at the location of \( q \) is zero.
- The electric field due to the second shell at the location of \( q \) is also zero.
Since the net electric field at the position of charge \( q \) is zero, the force acting on charge \( q \) can be calculated using the formula:
Force (F) = Charge (q) × Electric Field (E)
In this case, since \( E = 0 \), we find:
F = q × 0 = 0
Final Thoughts
Therefore, the net force on the charge \( q \) is zero. This illustrates a fundamental property of electric fields in spherical charge distributions and highlights the importance of understanding how charges interact in different configurations. In summary, the charge \( q \) experiences no net force due to the unique arrangement of the shells and their properties.
