How Much Should A Christian Rely on Physicians?

In 2 Chronicles 16:12 we come upon this verse regarding King Asa of Judah:

In the thirty-ninth year of his reign Asa was diseased in his feet, and his disease became severe. Yet even in his disease he did not seek the Lord, but sought help from physicians.

I believe it is wise and good to seek out medical advise and treatment, but is there a balance God desires when ailment comes upon us?

In James 5:13-15 we read these words:
Is anyone among you suffering? Let him pray. Is anyone cheerful? Let him sing praise. Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord. And the prayer of faith will save the one who is sick, and the Lord will raise him up. And if he has committed sins, he will be forgiven.

What is your view on listening to physicians and yet seeking God for healing?