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 righthand side of the above equation. In this sense, the choice of origin is irrelevant. ...
View
Full Document
 Spring '07
 k
 Vector Space, Charge, SEPTA Regional Rail, Musical notation, Yamaha YZFR1

Click to edit the document details