Short Answer 
The electric field at the center of a circular ring with uniform charge density can be determined using Coulomb’s law, which results in the formula E = ≈í¬™ / (2≈í¬µ‚ÄöCAR). Therefore, the correct expression for the electric field is option a: E = ≈í¬™ / (2≈í¬µ‚ÄöCAR).
Step 1: Understand the Electric Field Concept
The electric field is defined as a vector quantity that represents the influence of electric charges on the surrounding space. To determine the electric field at the center of a circular ring with a uniform charge density, we apply Coulomb’s law, which describes the force between charged objects. This law is fundamental in calculating the electric fields generated by various charge distributions.
Step 2: Apply Coulomb’s Law for a Circular Ring
To find the electric field (E) at the center of a circular ring, we use the formula derived from Coulomb’s law. For a ring with a uniform charge density (≈í¬™) and a radius (R), the electric field can be mathematically represented as:
- E = Œª / (2Œµ‚CAR)
This equation allows us to calculate the magnitude of the electric field using the parameters of the charge density and the radius of the ring.
Step 3: Identify the Correct Option
Based on the formula derived for the electric field at the center of a circular ring, you can easily identify which option corresponds to our findings. The correct expression for the electric field is:
- Option a: E = Œª / (2Œµ‚CAR)
Therefore, the answer to the question regarding the magnitude of the electric field at the center of a circular ring with uniform charge density is option a.