Electric_Field_Due_to_a_Point_Charge

Electric_Field_Due_to_a_Point_Charge - Electric Field Due...

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Unformatted text preview: Electric Field Due to a Point Charge ! ! ! Let us calculate the electric field E1 ( r2 ) at some observation point, r2 due to a source ! charge Q1 at r1 . The diagram below illustrates the situation. ! ! 1 kQ1 ! ! . E1 ( r2 ) = ! ! 3 (r2 ! r1 ) where k = 4 !" 0 r2 ! r1 Y ! ! ! r = r2 ! r1 Q1 ! r2 ! r1 ! r1 X We can express this as: ! ! ! ! kQ1 (r2 ! r1 ) kQ1 ^ E1 ( r2 ) = ! ! 2 ! ! = 2 r r r2 ! r1 r2 ! r1 Note that this notation is slightly different from that in the text on page 559 in that ! ! we have explicitly included the vector r2 in the argument of the function E1 . So ! ! ! E1 ( r2 ) is the electric field at r2 due to Q1. This field, however, depends only on the vector from the location of Q1 to our observation point. Note that: ^ 1. r always points from the source charge, Q1 towards the observation point. ! ! 2. If Q1 > 0, E1 ( r2 ) points away from Q1. ! ! 3. If Q1 < 0, E1 ( r2 ) points towards Q1. ! ! Specific example. r1 = !3, 2, 0 m, r2 = 5, 7, 0 m 8, 5, 0 ! ^ r = 8, 5, 0 m, r = 89 ! kQ1 E1 ( 5, 7, 0 ) = 8, 5, 0 N / C 3 (89) ! Note that the vector r2 does not explicitly appear on the right-hand side of the above equation. In this sense, the choice of origin is irrelevant. ...
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