Which nerve primarily supplies sensory function to the back of the hand?

The radial nerve is primarily responsible for the sensory function of the back of the hand. It innervates the skin in this area by supplying sensory fibers that provide the sense of touch, temperature, and pain to the dorsal aspect, particularly the thumb, index finger, and part of the middle finger. This is crucial for the skin's ability to communicate sensory information to the brain, which allows for appropriate responses and interactions with the environment.

Other nerves listed do have important roles but do not primarily supply sensory function to the back of the hand. The median nerve primarily serves the palmar side and parts of the thumb and first three digits, while the ulnar nerve supplies the little finger and part of the ring finger on the palm side. The musculocutaneous nerve mainly supplies motor function to the muscles of the front of the arm and provides sensory input to the lateral forearm, but it does not play a significant role in the sensory innervation of the back of the hand.