There are two pieces of plastic, a full ring (like this: 0 ) and a half ring (like this: ( . They have the same radius and charge density. Which electric field at the center has the greater magnitude? Defend your answer.

I want to say that the magnitudes are equal but I don't know if that's correct.

In the full ring, wouldn't the symettrical charge density cause the NET E to be zero? But in the half ring, the other half is missing....

So then the half ring would have the greater magnitude because the charge density does not cause the Net E to be zero?

absolutely correct.

Thank you

To determine which electric field at the center has the greater magnitude, we can use the principle of superposition. The principle of superposition states that the total electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge.

Let's consider the electric field at the center of each plastic piece separately:

1. Full ring (0): The electric field due to a full ring can be calculated using Coulomb's law, which states that the electric field produced by a charged object is directly proportional to the charge and inversely proportional to the distance squared. In this case, the full ring is symmetrical, so all contributions to the electric field from each point on the ring cancel out except for the contributions along the central axis. The resulting electric field at the center of the full ring is zero.

2. Half ring ( ): The electric field due to a half ring can also be calculated using Coulomb's law. Similar to the full ring, the contributions to the electric field from each point on the half ring cancel out except for the contributions along the central axis. However, since the half ring is missing a portion, there will be a net electric field at the center.

Since the electric field at the center of the full ring is zero, and the electric field at the center of the half ring is non-zero, we can conclude that the half ring has a greater magnitude of electric field at the center.

Therefore, your initial thoughts are incorrect in this case. The electric field at the center of the half ring has a greater magnitude than the electric field at the center of the full ring.