In order to obtain both the magnitude and direction

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In order to obtain both the magnitude and direction of the force on a charge, q 1 at position , experiencing a field due to the presence of another charge, q 2 at position , the full vector form of Coulomb's law is 2 r 2.2.2. Vector Fields

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15 2.2. Scalar and vector fields 1 q 2 q A graphical representation of Coulomb's law. You get a vector field if you keep fixed and move around and verify the Coulomb force at each location of . 2 q 2.2.2. Vector Fields
16 A visualization of the Coulomb force field could look like this: 2.2.2. Vector Fields

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17 Other examples for vector fields are The water velocity at each point in a river 2.2.2. Vector Fields
18 The gravitational pull of the earth 2.2.2. Vector Fields

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19 If the value (vector) assigned to a given point does not depend on the time when a (fictitious) measurement is made, the field is said to be stationary . If the value (vector) changes with time, then the field is said to be time-dependent . 2.2. Scalar and Vector Fields
20 In the following we will study the properties of scalar and vector fields, in particular arising from electromagnetic phenomena . However, the mathematical concepts used in our description are far more general , and can be used as well for describing different physical phenomena such as Fluid Flow , Elasticity , Traffic Control , Molecular Dynamics , … 2.2. Scalar and Vector Fields

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21 Further Reading: HELM modules 28.1 and 28.2.
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