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1/4 + 1/16 + 1/64 + 1/256 + ⋯. Archimedes' figure with a = 3 4 . In mathematics, the infinite series 1 4 + 1 16 + 1 64 + 1 256 + ⋯ is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC. [1] As it is a geometric series ...
Negative refraction. Negative refraction is the electromagnetic phenomenon where light rays become refracted at an interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a metamaterial which has been designed to achieve a negative value for (electric) permittivity ...
The first four partial sums of the series 1 + 2 + 3 + 4 + ⋯.The parabola is their smoothed asymptote; its y-intercept is −1/12. [1]The infinite series whose terms ...
e. The triboelectric effect (also known as triboelectricity, triboelectric charging, triboelectrification, or tribocharging) describes electric charge transfer between two objects when they contact or slide against each other. It can occur with different materials, such as the sole of a shoe on a carpet, or between two pieces of the same material.
Typical alkaline AA battery is about 5000 C ≈ 1.4 A⋅h: 10 4 ~ 9.65 × 10 4 C: Charge on one mole of electrons (Faraday constant) 10 5: 1.8 × 10 5 C: Automotive battery charge. 50Ah = 1.8 × 10 5 C: 10 6: mega-(MC) 10.72 × 10 6 C: Charge needed to produce 1 kg of aluminium from bauxite in an electrolytic cell: 10 7: 10 8: 5.9 × 10 8 C
The CODATA recommended value is −e/m e = −1.758 820 008 38 (55) × 10 11 C⋅kg −1. [2] CODATA refers to this as the electron charge-to-mass quotient, but ratio is still commonly used. There are two other common ways of measuring the charge-to-mass ratio of an electron, apart from Thomson and Dunnington's methods.
1/2 − 1/4 + 1/8 − 1/16 + ⋯. Demonstration that 1 2 − 1 4 + 1 8 − 1 16 + ⋯ = 1 3. In mathematics, the infinite series 1/2 − 1/4 + 1/8 − 1/16 + ⋯ is a simple example of an alternating series that converges absolutely . It is a geometric series whose first term is 1 2 and whose common ratio is − 1 2, so its sum is.
The elementary charge, usually denoted by e, is a fundamental physical constant, defined as the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 e. [ 2][ a] In the SI system of units, the value of the elementary charge is exactly ...