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Electric Fields

All charges create an electric field which surrounds it. The E-field is what is responsible for exerting an electric force on charges placed near another charge. Like force, the E-field created by a charge is a vector, meaning it has both a direction and a magnitude. The directionality of an E-field is always away from a positive charge and towards a negative charge. The E-field at a specific location can be calculated by dividing the electric force experienced on a test charge at that location by the value of that test charge.

E=F/q

Protons will accelerate in the direction of the E-field, while electrons will accelerate opposite to the direction of the E-field.

Test charge in an E-field
An example of an E-field from a point charge.


Note that in the above example, 'r' is the radial distance between the test charge and the charge whose E-field we are concerning.

Deriving the E-field due to a line of uniform charge

Knowing the E-field created by a singular point-charge allows us to derive the E-field a distance away from a line of uniform charge density λ.

Test charge in an E-field


Deriving the E-field due to a hoop of uniform charge

Similarly to finding the E-field due to a line of uniform charge, we can calculate the E-field at a specified distance away from a hoop of uniform charge.