**Core Concept**
The sensory nerve supply to the capsule of the temporomandibular joint (TMJ) is crucial for the perception of pain, proprioception, and other sensations in the joint and surrounding structures. The TMJ is a complex joint with both fibrous and synovial components, and its nerve supply reflects this complexity.

**Why the Correct Answer is Right**
The correct answer is the auriculotemporal nerve, which is a branch of the mandibular division of the trigeminal nerve (CN V3). The auriculotemporal nerve provides sensory innervation to the TMJ capsule, as well as the surrounding skin and muscles of mastication. This nerve is particularly important for the transmission of pain signals from the joint, which can be a common source of referred pain in the face and head.

• The auriculotemporal nerve arises from the mandibular nerve, which is itself a branch of the trigeminal nerve.
• The auriculotemporal nerve runs anteriorly to the TMJ, where it provides sensory innervation to the capsule and surrounding structures.
• The auriculotemporal nerve also carries parasympathetic fibers from the otic ganglion, which innervate the parotid gland.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the inferior alveolar nerve primarily provides sensory innervation to the lower teeth and surrounding bone, rather than the TMJ.
**Option B:** This option is incorrect because the lingual nerve primarily provides sensory innervation to the tongue, rather than the TMJ.
**Option C:** This option is incorrect because the glossopharyngeal nerve (CN IX) primarily provides sensory innervation to the pharynx and soft palate, rather than the TMJ.

**Clinical Pearl / High-Yield Fact**
The auriculotemporal nerve is a common source of referred pain in the face and head, particularly in patients with temporomandibular joint disorders (TMDs). This pain can be referred to the ear, temple, or even the eye, and is often associated with clicking or popping of the TMJ.

**Correct Answer:** C.