Electric Charges and Fields

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Electric Field

The electric field E at a point is defined as the electric force F experienced by a positive test charge q0 placed at that point divided by the magnitude of the test charge

straight E space equals space straight F over straight q subscript 0

The electric field E is a vector quantity and has the same direction as the electric force F. The electric field is due to an external charge and not due to the
test charge.

Electric field due to a system of charges

Superposition principle will use determine electric field at a point P. According to the superposition principle, the total electric field at a point in space is equal to the vector sum of individual fields present.

straight E subscript 1 space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction straight q subscript 1 over straight r subscript 1 straight P end subscript straight r with hat on top subscript 1 straight P end subscript
straight E subscript 2 space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction straight q subscript 2 over straight r subscript 2 straight P end subscript straight r with hat on top subscript 2 straight P end subscript
Since space straight E space left parenthesis straight r right parenthesis space equals space straight E subscript 1 space plus space straight E subscript 2 space plus space straight E subscript 3 space plus space... space straight E subscript straight n
straight E space left parenthesis straight r right parenthesis space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction begin inline style sum from straight i space equals space 1 to straight n of end style fraction numerator qi over denominator straight r subscript ip superscript 2 end fraction straight r with hat on top subscript iP

The electric field at a point due to a system of charges is the vector sum of the electric fields at the point due to individual charges.

 

Physical significance of electric field

  1. The electric field is an elegant way of characterising the electrical environment of a system of charges.
  2. The electric field is a characteristic of the system of charges and is independent of the test charge that you place at a point to determine the field.