Charges of 2 uC and 3 uC are 0.1 m apart. Find the force between them — Physics problems | PhysLabo
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Coulomb's force between two charges

Medium 10 grade Electricity / Electrostatics

Two point charges $q_1 = 2$ uC and $q_2 = 3$ uC are placed $r = 0.1$ m apart. Find the electrostatic force between the charges. Coulomb's constant is $k = 9 \cdot 10^9$ N·m²/C².

Given
  • $q_1 = 2$ uC $= 2 \cdot 10^{-6}$ C
  • $q_2 = 3$ uC $= 3 \cdot 10^{-6}$ C
  • $r = 0.1$ m
  • $k = 9 \cdot 10^9$ N·m²/C²
  • $F = ?$
Hints
Hint 1 / 2
Convert the charges to coulombs ($1$ uC $= 10^{-6}$ C) and the distance to meters.
Hint 2 / 2
Coulomb's constant is $k = 9 \cdot 10^9$ N·m²/C²; the distance is squared in the denominator.
Solution

Coulomb's law:

$$F = k \frac{q_1 q_2}{r^2} = 9 \cdot 10^9 \cdot \frac{2 \cdot 10^{-6} \cdot 3 \cdot 10^{-6}}{(0.1)^2}$$

$$F = 9 \cdot 10^9 \cdot \frac{6 \cdot 10^{-12}}{10^{-2}} = \frac{54 \cdot 10^{-3}}{10^{-2}} = 5.4 \text{ N}$$

Answer

$F = 5.4$ N