Find the magnitude and direction of the total electric field due to the two point charges, q₁ and q₂, at the origin of the coordinate system as shown in Figure 18.21.

Strategy

Since the electric field is a vector (having magnitude and direction), we add electric fields with the same vector techniques used for other types of vectors. We first must find the electric field due to each charge at the point of interest, which is the origin of the coordinate system (O) in this instance. We pretend that there is a positive test charge, , at point O, which allows us to determine the direction of the fields E₁ and E₂. Once those fields are found, the total field can be determined using vector addition.

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Etot 1.26 x 105 N/C E₁ = 1.13 x 105 N/C 63.4% E₂ = 0.56 x 105 N/CO 4.00 cm 2.00 cm 9₁ = +5.0 nC 9/2 = +10 nC -X