A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have  equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the  symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field,...

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...

The somatosensory system relays sensory information from the skin, mucous membranes, limbs, and joints. Somatosensation is more familiarly known as the sense of touch. A typical somatosensory pathway includes three types of long neurons: primary, secondary, and tertiary. Primary neurons have cell bodies located near the spinal cord in groups of neurons called dorsal root ganglia. The sensory neurons of ganglia innervate designated areas of skin called dermatomes.

Each cerebral hemisphere can be divided into three main regions. The outermost region, the cerebral cortex, is a thin layer (2 to 4 millimeters thick) made up of gray matter, consisting of neuron cell bodies, dendrites, glial cells, and blood vessels. The middle region, or white matter, is primarily composed of myelinated nerve fibers organized into three types of large tracts: association fibers, commissures, and projection fibers. Association fibers connect different areas within the same...

The cerebral cortex, the brain's outermost layer, is pivotal in processing complex cognitive tasks, emotions, and various sensory inputs and executing voluntary motor activities. This intricate structure is divided into three primary functional areas: the motor areas, sensory areas, and association areas.
Motor Areas
The motor areas located in the frontal lobe are central to controlling voluntary movements. This region is further subdivided into the primary motor cortex and the premotor cortex....

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...