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Question
Two small spheres 18 cm apart have equal negative charges and repel each other with the force of 6 × 10-3 N. Find the total charge on both spheres.
Solution
Given: F = 6 × 10-3 N, r = 18 cm = 18 × 10-2 m
To find: Total charge (q1 + q2)
Formula: F = `1/(4πε_0)("q"_1"q"_2)/"r"^2`
f = `(9 xx 10^9 xx "q"^2)/(18 xx 10^(-2))^2`
`(f xx (18 xx 10^(-2))^2)/(9 xx 10 ^9) = "q"^2`
q2 = `(6 xx 10^(-8) xx 18 xx 18 xx 10^(-4))/(10^9)`
q2 = `(6 xx 36 xx 10^(-12))/(10^9)`
∴ q2 = 216 × 10-21
q2 = 21.6 × 10-20
q = `sqrt(21.6 xx 10^-20))`
∴ q = 4.648 × 10-10 C
∴ q = -4.648 × 10-10 C
∴ Total charge = 2q
= 2 × (-4.648 × 10-10)
= 9.296 × 10-10 C
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