F 23 = k q 2 q 3 4 2 = 9 × 1 0 9 × 4 × 6 × 1 0 − 18 16 F 23 = − 13.5 × 1 0 − 9 N F 23 x = − 13.5 × 1 0 − 9 N F 23 y = 0 F 13 = k q 1 q 2 5 2 = 9 × 1 0 9 × 8 × 6 × 1 0 − 18 25 F 13 = 17.28 × 1 0 − 9 N F 13 x = F 13 × c o s ( 37 ) = 17.28 × 1 0 − 9 × 0.7986 = 13.799 × 1 0 − 9 N F 13 y = F 13 × s i n ( 37 ) = 17.28 × 1 0 − 9 × 0.6018 = 10.399 × 1 0 − 9 N F_{23} = \frac{kq_2q_3}{4^2} = \frac{9 \times 10^9 \times 4 \times 6 \times 10^{-18}}{16} \\
F_{23} = -13.5 \times 10^{-9} \;N \\
F_{23x}= -13.5 \times 10^{-9} \;N \\
F_{23y}= 0 \\
F_{13} = \frac{kq_1q_2 }{5^2} = \frac{9 \times 10^9 \times 8 \times 6 \times 10^{-18}}{25} \\
F_{13} = 17.28 \times 10^{-9} \;N \\
F_{13x} = F_{13} \times cos(37) = 17.28 \times 10^{-9} \times 0.7986 = 13.799 \times 10^{-9} \;N \\
F_{13y} = F_{13} \times sin (37) = 17.28 \times 10^{-9} \times 0.6018 = 10.399 \times 10^{-9} \;N F 23 = 4 2 k q 2 q 3 = 16 9 × 1 0 9 × 4 × 6 × 1 0 − 18 F 23 = − 13.5 × 1 0 − 9 N F 23 x = − 13.5 × 1 0 − 9 N F 23 y = 0 F 13 = 5 2 k q 1 q 2 = 25 9 × 1 0 9 × 8 × 6 × 1 0 − 18 F 13 = 17.28 × 1 0 − 9 N F 13 x = F 13 × cos ( 37 ) = 17.28 × 1 0 − 9 × 0.7986 = 13.799 × 1 0 − 9 N F 13 y = F 13 × s in ( 37 ) = 17.28 × 1 0 − 9 × 0.6018 = 10.399 × 1 0 − 9 N
Total force:
F x = F 23 x + F 13 x = − 13.5 × 1 0 − 9 + 13.799 × 1 0 − 9 = 0.299 × 1 0 − 9 N F y = F 23 y + F 13 y = 0 + 10.399 × 1 0 − 9 = 10.3399 × 1 0 − 9 N M a g n i t u d e = F x 2 + F y 2 = 1.0344 × 1 0 − 8 N F_x=F_{23x}+F_{13x}=-13.5 \times 10^{-9} + 13.799 \times 10^{-9} = 0.299 \times 10^{-9} \; N \\
F_y=F_{23y}+F_{13y}= 0 + 10.399 \times 10^{-9} = 10.3399 \times 10^{-9} \; N \\
Magnitude= \sqrt{F_x^2+F_y^2}= 1.0344 \times 10^{-8} \;N F x = F 23 x + F 13 x = − 13.5 × 1 0 − 9 + 13.799 × 1 0 − 9 = 0.299 × 1 0 − 9 N F y = F 23 y + F 13 y = 0 + 10.399 × 1 0 − 9 = 10.3399 × 1 0 − 9 N M a g ni t u d e = F x 2 + F y 2 = 1.0344 × 1 0 − 8 N
angle with +ve x axis = a r c t a n ( F y F x ) = 72.07 d e g r e e s =arctan(\frac{F_y}{F_x})= 72.07 \; degrees = a rc t an ( F x F y ) = 72.07 d e g rees
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