Question

A charge +q exerts a force of magnitude -0.2 N on another change -2q. If they are separated by 25.0 cm, determine the value of q.

Answer 1

Given: q₁ = + q, q₂ =−2q, F = – 0.2 N, r = 25 cm = 25 × 10⁻² m

To find: Charge (q)

Formula: F = `1/(4πε_0)("q"_1"q"_2)/"r"^2`

Calculation: From formula,

– 0.2 = `(9xx10^9xx"q"xx(-2"q"))/((25xx10^-2)^2)`

∴ `(- 0.2)/(- 2) xx (25 xx 10^-2)^2/(9 xx 10^9) = "q"^2`

∴ `0.1 xx (25 xx 10^-2)^2/(9 xx 10^9) = "q"^2`

∴ `1/10 xx (25 xx 10^-2)^2/(9 xx 10^9) = "q"^2`

`∴ (25 xx 10^-2)^2/(9 xx 10^10) = "q"^2`

∴ `sqrt((25 xx 10^-2)^2/(9 xx 10^10))` = q

∴ `(25 xx 10^-2)/(3 xx 10^5)` = q

∴ q = 8.33 × 10⁻⁷ C 

or q = 0.833 × 10⁻⁶ C

∴ q = 0.833 μC