Sure! Below is a Python function to generate test cases for the given problem statement.

```python
import random

def generate_test_case():
    # Set the constraints
    N = random.randint(1, 10**5)
    S = ''.join(random.choice(['B', 'W']) for _ in range(2 * N))
    
    return N, S

# Example usage
if __name__ == "__main__":
    N, S = generate_test_case()
    print(N)
    print(S)
```

### Explanation
1. **N Generation**:
    - `N` is randomly chosen between 1 and \(10^5\).

2. **String S Generation**:
    - `S` is generated as a string of length `2N` where each character is randomly chosen to be either 'B' (black) or 'W' (white).

### Example Output
When you run the function, it will provide an output like:
```
74820
BWBWBWWBBWB...WWBWBWBW
```

This satisfies the constraints given in the problem statement.

### Note
Given the large possible values for `N`, running this in an environment with limited resources could take significant memory and time. For testing purposes, you may want to start with smaller values of `N` and verify the correctness of your solution incrementally with larger inputs.