Question

Chapter 22, Problem 007 In the fogue the four artises form a sauare of ege lernha 2 20 cm and have cdharoe -9,16 n, -21.4 nC, 3-214 nC, and q 9.16 nc. what s the magnitude of the net electric field produced by the partides at the square's center? --2 1.4 nC, 43-21.4 nC, and q4 “-9.16 nc. what is the 91 Number Units the tolerance is +/-2%

Answer 1

THINK Our system consists of four point charges that are placed at the corner of a square. The total electric field at a point is the vector sum of the electric fields of individual charges EXPRESS Applying the superposition principle, the net electric field at the center of the square is 4 4 i-1 With 41-+9.16nC, q2ーー21.41C, q3-+21.4DC, and q4--916nC, the x component of the electric field at the center of the square is given by, taking the signs of the charges into consideration, g21 cos 45 91 4tEo Similarly, the y component of the electric field is 91 192 4cos 45° 4TE The magnitude of the net electric field is E JE2 E

ANALYZE Substituting the values given, we obtain 9.16nC +21.4nC-21.4nC-9.16nC)0 an E., -9.16nC +21.4 nC+21.4nC-9.16nC 2. (8.99 x 10" N·m2 /C2)(245x10" CN2 (0.0720 m) -0.60x10° NC. Thus, the electric field at the center of the square is E-Ej-(0.60x105 N/C). LEARN The net electric field at the center of the square is depicted in the figure below (not to scale). The field, pointing to the +y direction, is the vector sum of the electric fields of individual charges 92 E.

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