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Question

Two charges 2.0 × 10−6 C and 1.0 × 10−6 C are placed at a separation of 10 cm. Where should a third charge be placed, such that it experiences no net force due to these charges?

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Solution

Given:
q1=2.0×10-6 Cq2=1.0×10-6 C
Let the third charge, q, be placed at a distance of x cm from charge q1, as shown in the figure.



By Coulomb's Law, force,
F=14πε0Q1Q2r2
Force on charge q due to q1,
F=9×109×2.0×10-6×qx2
Force on charge q due to q2,
F'=9×109×10-6×q10-x2
According to the question,
F-F'=0
F=F'9×109×2×10-6×qx2=9×109×10-6×q10-x2x2=210-x2x2-40x+200=0x=20±102x=5.9 cm ( x20+102)
So, the third charge should be placed at a distance of 5.9 cm from q1.

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