The potential of a long hollow cylinder is the measure of the electric potential energy per unit charge at any point inside or outside the cylinder. It is affected by the charge distribution and the distance from the center of the cylinder.
The potential of a long hollow cylinder can be calculated using the formula V = k * λ * ln(r2/r1), where V is the potential, k is the Coulomb constant, λ is the charge per unit length of the cylinder, and r2 and r1 are the outer and inner radii of the cylinder respectively.
The electric field of a long hollow cylinder is directly proportional to the potential gradient. This means that the electric field increases as the potential increases and decreases as the potential decreases. The electric field is also inversely proportional to the distance from the center of the cylinder.
Inside a long hollow cylinder, the potential is constant and equal to the potential at the surface of the cylinder. Outside the cylinder, the potential decreases as the distance from the center of the cylinder increases. This is because the electric field decreases with distance from the cylinder, causing a decrease in potential.
One practical application is in the design of capacitors, where a long hollow cylinder can act as one of the plates. The potential of the cylinder is important in determining the capacitance and overall performance of the capacitor. It is also useful in understanding the behavior of charged particles inside and outside the cylinder, which has implications in areas such as plasma physics and particle accelerators.