Electric Potential: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Electric Potential. Understanding the underlying formula is key to arriving at the correct answer below:

The electric potential \( V \) at the center of a charged half-ring is given by:

\[
V = \frac{1}{4\pi \epsilon_0} \int \frac{\lambda \, dl}{r}
\]

For a half-ring of radius \( r \), the total length is \( \pi r \), and the potential at the center is:

\[
V = \frac{\lambda}{4\pi \epsilon_0} \cdot \pi r \cdot \frac{1}{r} = \frac{\lambda}{4\epsilon_0}
\]

Thus, the electric potential at the center of the half-ring is:

\[
V = \frac{\lambda}{4 \epsilon_0}
\]