# Often this scalar value describes some physical

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Often this scalar value describes some physical quantity which (ideally) can be measured at this point. Even if such a measurement is not done in practice, a fictitious measurement can be imagined which would give us this value. 2.2. Scalar and Vector Fields

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11 2.2.1. Scalar Fields Examples for scalar fields are: The temperature at each point in this lecture theatre. The charge density at each point inside a cathode ray tube. The pressure at each point in the atmosphere above Manchester. The total X-ray radiation exposure of each point in the body during a routine CT. 2.2. Scalar and Vector Fields
12 2.2.1. Scalar Fields Example for a scalar field in 2D: Each point of the plate is assigned exactly one real number, which describes the temperature at this point.

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13 2.2.2. Vector fields A vector field is a distribution of vectors over a region of space such that a vector is associated with each point of the region. Also these vectors often describe physical quantities which (ideally) can be measured (sometimes in a fictitious experiment) at every point. Each of these measurements can be thought of having a magnitude and a direction which both are characteristic for each point.
14 Example: Coulomb Force 2 1 4 3 2 1 0 2 1 r r r r q q F - - = π ε 1 r Coulomb's law is a law of physics describing the electrostatic interaction between electrically charged particles.

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