Question

What charge placed 9 cm from a charge of 100 uC will produce a force of 1/9 N in air?

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Answer 1

Explanation:

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Answer 2

Given :

Charge 1 (Q₁) = 100 μC = 100 × 10⁻⁶ C

Force (F) = $\frac{1}{9}$ N

To Find :

What charge placed 9 cm from a charge of 100 μC will produce a force of 1/9 N in air

Solution :

The formula for electrostatic force in vacuum/air is -

 Force (F) = $\frac{1}{4\pi E_o}$$\frac{Q_1Q_2}{r^2}$

Where, Q₁, Q₂ = charges and r = distance between the charges

So,

 Force (F)     =   $\frac{1}{4\pi E_o}$$\frac{Q_1Q_2}{r^2}$

⇒  $\frac{1}{9}$               = 9 × 10⁹ × $\frac{100 *10^-^6* Q_2}{(9 * 10^-^2)^2}$

⇒  $\frac{1}{9}$               = 9 × 10⁹ ×  $\frac{10^-^4 Q_2}{9 * 9 * 10^-^4}$

⇒  Q₂            = $\frac{1}{10^9}$

∴   Q₂            = 10⁻⁹ C

Hence the charge is 10⁻⁹ C or 1 nC