F A B = k q 1 q 2 r A B 2 = k × 1 0 2 × 1 0 2 2 2 = k × 1 0 4 4 F_{AB}=\frac{kq_1q_2}{r_{AB}^2}=\frac{k\times10^2\times10^2}{2^2}=\frac{k\times10^4}{4} F A B = r A B 2 k q 1 q 2 = 2 2 k × 1 0 2 × 1 0 2 = 4 k × 1 0 4
F C B = k q 1 q 2 r C B 2 = k × 1 0 2 × 1 0 2 2 2 = k × 1 0 4 4 F_{CB}=\frac{kq_1q_2}{r_{CB}^2}=\frac{k\times10^2\times10^2}{2^2}=\frac{k\times10^4}{4} F CB = r CB 2 k q 1 q 2 = 2 2 k × 1 0 2 × 1 0 2 = 4 k × 1 0 4
F n e t = F n e t ′ + F D B F_{net}=F'_{net}+F_{DB} F n e t = F n e t ′ + F D B
F D B = k q 1 q 2 r D B 2 = k × 1 0 2 × 1 0 2 ( 2 2 ) 2 = k × 1 0 4 8 F_{DB}=\frac{kq_1q_2}{r_{DB}^2}=\frac{k\times10^2\times10^2}{(2\sqrt2)^2}=\frac{k\times10^4}{8} F D B = r D B 2 k q 1 q 2 = ( 2 2 ) 2 k × 1 0 2 × 1 0 2 = 8 k × 1 0 4
F n e t ′ = F A B 2 + F C B 2 = 2 F A B F'_{net}=\sqrt{F_{AB}^2+F_{CB}^2}=\sqrt{2}F_{AB} F n e t ′ = F A B 2 + F CB 2 = 2 F A B
F n e t ′ = 2 k × 1 0 4 4 F'_{net}=\sqrt{2}\frac{k\times10^4}{4} F n e t ′ = 2 4 k × 1 0 4
F n e t = F n e t ′ + F D B = ( 2 + 1 2 ) k × 1 0 4 4 F_{net}=F'_{net}+F_{DB}=(\sqrt{2}+\frac{1}{2})\frac{k\times10^4}{4} F n e t = F n e t ′ + F D B = ( 2 + 2 1 ) 4 k × 1 0 4 F n e t = ( 2 2 + 1 ) 9 × 1 0 13 8 N F_{net}=(2\sqrt{2}+1)\frac{9\times10^{13}}{8}N F n e t = ( 2 2 + 1 ) 8 9 × 1 0 13 N
Comments
A very good answer. Thank you very much.
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