C

Step 1: Evaluate (i) Magnetic flux density due to a current carrying circular coil. The magnetic flux density at the center of a circular coil is maximum and decreases as we move away, hence it cannot be zero. Therefore, not matching with [A].
Step 2: Evaluate (ii) Magnetic flux density at a point on a current carrying thin wire. The magnetic flux density varies and can be maximum at the wire's center or decrease to zero. Hence, matches with [B].
Step 3: Evaluate (iii) Electric field strength due to a uniformly charged ring. The electric field strength along the axis decreases continuously as we move away from the center, matching with [C].
Step 4: Evaluate (iv) Electric potential due to a uniformly charged ring. The electric potential continuously increases as we move away from the center into a definite distance along the axis, matching with [D].

Therefore, the correct matches are: (i) - (B), (ii) - (C), (iii) - (D), (iv) - (A). Thus, the final correct answer is C.