Two charges are located on the positive x-axis of a coordinate system. Charge ๐1 = 2 ร 10โ9๐ถ is 2cm from the origin, and charge ๐2 = โ3 ร 10โ9๐ถ is 4cm from the origin. What is the total force exerted by these two charges on a charge ๐3 = 5 ร 10โ9๐ถ located at the origin?
Solution.
"q_1=2\\sdot10^{-9}C;\nr_1=0.02m;"
"q_2=-3\\sdot10^{-9}C; r_2=0.04m;"
"F_{13}=k \\dfrac{q_1\\sdot q_3}{r_1^2};"
"F_{13}=9\\sdot10^9\\dfrac{2\\sdot10^{-9}\\sdot5\\sdot10^{-9}}{0.02^2}=2.25\\sdot10^{-4}N;"
"F_{23}=k\\dfrac{q_2\\sdot q_3}{r_2^2};"
"F_{23}=9\\sdot10^9\\dfrac{3\\sdot10^{-9}\\sdot5\\sdot10^{-9}}{0.04^2}=0.84\\sdot10^{-4}N;"
"F=F_{13}-F_{23}=2.25\\sdot 10^{-9} - 0.84\\sdot 10^{-9}=1.41\\sdot10^{-9}N;"
Answer: "F=1.41\\sdot10^{-9}N."
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