Answer to Question #294694 in Optics for sarah

Question #294694

In the figure above, q1 = 6.53 nC, q2 = 13.1 nC, and q3 = 13.1 nC. If the net force on q1 is 0, then what would q be?


1
Expert's answer
2022-02-07T15:26:00-0500

Force


F3=kq1q3a2=9×109×13.1×109×qa2F_3=\frac{kq_1q_3}{a^2}=\frac{9\times10^9\times13.1\times10^{-9}\times q}{a^2}

F2=kq1q2a2=9×109×13.1×109×qa2F_2=\frac{kq_1q_2}{a^2}=\frac{9\times10^9\times13.1\times10^{-9}\times q}{a^2}

Net force

Fnet=2F2F_{net}=\sqrt{2}F_2

F1=kq1q2a2=9×109×6.53×109×q2a2F_1=\frac{kq_1q_2}{a^2}=\frac{9\times10^9\times6.53\times10^{-9}\times q }{2a^2}


Fnet=2kq1q2a2=2×9×109×6.53×109×13.1×109a2F'_{net}=\sqrt{2}\frac{kq_1q_2}{a^2}=\sqrt{2}\times\frac{9\times10^9\times6.53\times10^{-9}\times13.1\times10^{-9}}{a^2}

Fnet=(2×6.53+12×q×109)×13.1×1018F_{net}=({\sqrt{2}\times6.53+\frac{1}{2}\times q\times10^{-9}})\times13.1\times10^{-18}

Fnet=0F_{net}=0

(2×6.53×109+12×q)=0({\sqrt{2}\times6.53\times10^{-9}+\frac{1}{2}\times q})=0

q=18.46×109Cq=-18.46\times10^{-9}C


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