Which statement is true :-
(i) A ring of radius R carries a uniformly distributed charge +Q. A point charge -q is placed on the axis of the ring at a distance 2R from the centre of the ring and released from rest. The particle executes a smiple harmonic motion along the axis of the ring.
(ii) Electrons move from a region of higher potential to that of lower potential

Options

A. only (i)
B. only (ii)
C. (i), (ii)
D. none of them

Answer

To solve the question, we need to analyze both statements provided in the question:

### Statement (i):
"A ring of radius R carries a uniformly distributed charge +Q. A point charge -q is placed on the axis of the ring at a distance 2R from the center of the ring and released from rest. The particle executes a simple harmonic motion along the axis of the ring."

**Step 1: Understanding the Setup**
- We have a ring with a radius \( R \) that has a uniformly distributed positive charge \( +Q \).
- A negative point charge \( -q \) is placed on the axis of the ring at a distance \( 2R \) from the center of the ring.

**Step 2: Analyzing Forces on the Charge**
- When the charge \( -q \) is released, it will experience a force due to the electric field created by the ring.
- The symmetry of the ring means that the horizontal components of the forces from opposite sides will cancel out, leaving only the axial component of the force acting on the charge.

**Step 3: Direction of the Force**
- Since the charge \( -q \) is negative and the ring has a positive charge, the force acting on \( -q \) will be directed towards the ring (attractive force).
- As the charge moves towards the center of the ring, it will accelerate due to the force acting on it.

**Step 4: Motion Analysis**
- When the charge \( -q \) crosses the center of the ring, it will continue to move due to inertia, but the direction of the force will change, pulling it back towards the center.
- This back-and-forth motion around the center of the ring is characteristic of simple harmonic motion (SHM).

**Conclusion for Statement (i):**
- The charge \( -q \) will indeed execute simple harmonic motion along the axis of the ring. Thus, statement (i) is **true**.

### Statement (ii):
"Electrons move from a region of higher potential to that of lower potential."

**Step 1: Understanding Electric Potential**
- Electric potential is defined such that positive charges move from higher potential to lower potential.
- However, electrons are negatively charged particles.

**Step 2: Direction of Electron Movement**
- Since electrons are negatively charged, they will move in the opposite direction of the electric field.
- Therefore, electrons actually move from regions of lower potential to regions of higher potential.

**Conclusion for Statement (ii):**
- The statement is incorrect. Electrons do not move from higher potential to lower potential; they move from lower potential to higher potential. Thus, statement (ii) is **false**.

### Final Answer:
- The correct statement is (i) only.