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.

Answer 1

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^(-3) xx 18 xx 18 xx 10^(-4))/(9 xx 10^9)`

∴ q² = `(6 xx 324 xx 10^(-7))/(9 xx 10^9)`

= `(1944 xx 10^(-7))/(9 xx 10^9)`

= `(1944 xx 10^(-7) xx 10^-9)/(9)`

= `(1944 xx 10^(-16))/(9)`

= 216 × 10⁻¹⁶

= 216 × 10⁻¹⁶

q² = 216 × 10⁻¹⁶

q = `sqrt(216 xx 10^-16))`

∴ q = 14.7 × 10⁻⁸ C

∴ q = 1.47 × 10⁻⁷ C

∴ Total charge = (q + q)

= 2q

= 2 × (1.47 × 10⁻⁷)

= 2.94 × 10⁻⁷ C