Excitable cells are commonly studied via the extracellular potentials (EPs) they generate, which underlie signals in electroencephalography (EEG), electrocardiography (ECG), and multielectrode array (MEA) recordings. However, some excitable systems produce little or no detectable EPs, for reasons that remain poorly understood. Here we show mathematically that homogeneous excitable cells and tissues -- with spatially uniform ion channel distributions and no external stimulation -- are extracellularly silent even in the presence of full action potentials. Specifically, an isolated, autonomous cell with uniform membrane properties generates zero EP, independent of shape, kinetics, or model complexity. The result extends to coupled cells provided the tissue remains fully homogeneous. EPs emerge only from spatial inhomogeneities, propagating electrical waves, or applied currents. We demonstrate the physiological relevance of this principle in Purkinje neurons, where clustering of sodium channels enables ephaptic synchronization, while uniform cells remain asynchronous and undetectable extracellularly. We further show that connected human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) and pancreatic {beta}-cells exhibit EPs in proportion to cellular or tissue-level heterogeneity. These findings offer a unifying explanation for the observed silence of some excitable cells and are consistent with experimental reports of strong intracellular signals accompanied by weak or absent EPs.