**Given Information:**

- Two rings of radii 5m and 10m
- The rings move in opposite directions with velocities of 20m/s and 10m/s respectively
- The rings are on a conducting surface S
- There is a uniform magnetic field of magnitude 0.1 T perpendicular to the plane of the rings

**To Find:**

The potential difference between the highest points of the two rings.

**Solution:**

1. The motion of the rings creates an induced electric field due to the change in magnetic flux through the rings. According to Faraday's law of electromagnetic induction, the magnitude of the induced electric field is given by:

E = -dΦ/dt

Where E is the induced electric field, Φ is the magnetic flux, and t is time.

2. The induced electric field causes charges to accumulate at the ends of the rings, creating an electric potential difference between the highest points of the rings.

3. The induced electric field is given by:

E = -vB

Where E is the induced electric field, v is the velocity of the rings, and B is the magnetic field.

4. The magnitude of the induced electric field is the same for both rings, but the direction is opposite due to their opposite velocities.

5. Since the rings are on a conducting surface, the charges move freely along the rings. Therefore, the induced electric field causes a redistribution of charges, resulting in a potential difference between the highest points of the rings.

6. The potential difference between the highest points of the rings is given by:

ΔV = Ed

Where ΔV is the potential difference, E is the induced electric field, and d is the distance between the highest points of the rings.

7. Substituting the values, we get:

ΔV = (-vB)d

For the first ring with a radius of 5m and velocity of 20m/s:

ΔV1 = (-20m/s)(0.1T)(2π(5m))

For the second ring with a radius of 10m and velocity of 10m/s:

ΔV2 = (-10m/s)(0.1T)(2π(10m))

8. Calculating the values:

ΔV1 = -628.32 V

ΔV2 = -1256.64 V

9. The negative sign indicates that the potential difference is negative, which means that the highest point of the second ring is at a lower potential than the highest point of the first ring.

**Answer:**

The potential difference between the highest points of the two rings is -628.32 V.