NEET Physics Question - Electrostatics

A half-ring of radius r has linear charge density λ. The electric potential at the centre of the half-ring is

\[ \frac{\lambda}{4\varepsilon_{0}}\]

\[ \frac{\lambda}{4\pi^{2}\varepsilon_{0}r}\]

\[ \frac{\lambda}{4\pi\varepsilon_{0}r}\]

\[ \frac{\lambda}{4\varepsilon_{0}r}\]

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:

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

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