5.2: Electric Field Due to Point Charges
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The electric field intensity associated with a single particle bearing charge q1, located at the origin, is (Section 5.1)
E(r)=ˆrq14πϵr2
If this particle is instead located at some position r1, then the above expression may be written as follows:
E(r;r1)=r−r1|r−r1| q14πϵ|r−r1|2
or, combining like terms in the denominator:
E(r;r1)=r−r1|r−r1|3 q14πϵ
Now let us consider the field due to multiple such particles. Under the usual assumptions about the permittivity of the medium (Section 2.8), the property of superposition applies. Using this principle, we conclude:
The electric field resulting from a set of charged particles is equal to the sum of the fields associated with the individual particles.
Stated mathematically:
E(r)=N∑n=1E(r;rn) where N is the number of particles. Thus, we have
E(r)=14πϵN∑n=1r−rn|r−rn|3 qn