Question Analysis: Assertion (A) and Reason (R) type question.
Step 1 (Governing Principle): [0.25 Mark]
The electric field $\vec{E}$ at the center of a charged ring is determined by the principle of superposition. For a semi-circular ring with uniform charge density $\lambda$, the electric field at the center is given by:
$$E = \frac{2k\lambda}{R} = \frac{2}{4\pi\epsilon_0} \cdot \frac{\lambda}{R}$$The potential $V$ at the center of a ring is a scalar quantity given by $V = \int \frac{k \, dq}{r}$.
Step 2 (Step-by-Step Mathematical Working): [0.50 Mark]
- Assertion (A): The positive half creates an electric field directed away from it, and the negative half creates an electric field directed towards it. Both vectors point in the same direction (along the axis of symmetry OC), resulting in a non-zero resultant field. Thus, Assertion (A) is True.
- Reason (R): The potential at the center $O$ is the algebraic sum of potentials due to the positive and negative halves. Since the charges are equal and opposite and equidistant from the center, $V_{total} = V_+ + V_- = \frac{kQ}{R} + \frac{k(-Q)}{R} = 0$. The reason states the potential is not zero, which is mathematically incorrect. Thus, Reason (R) is False.
Step 3 (Final Concluded Answer): [0.25 Mark]
Correct Option: Assertion (A) is true, but Reason (R) is false.
💡 EL10 Concept Insight:
Think of the electric field like a "push" or "pull" force—the positive side pushes and the negative side pulls in the same direction, so they add up! However, electric potential is just a "number" (like a bank balance); since you have the same amount of positive and negative charge, they perfectly cancel each other out to zero.