Question

Two identical positive charges exert a repulsive force of 6.4x10-'N when separated by a distance of3.8x10-10 m. Calculate the charge of each.

Answer 1

ANSWER

3.2 · 10⁻¹⁵ C

EXPLANATION

By Coulomb's law,

$F=k_e\cdot\frac{q_1\cdot q_2}{r^2}$

Where

• F: the force exerted between the charges,

,

• q1 and q2: charges

,

• r: distance between the charges

,

• ke: Coulomb's constant (approximately 8.988x10⁹ N*m²/C²)

In this problem, we know that the charges are identical, thus,

$q_1=q_2=q$$F=k_e\cdot\frac{q^2}{r^2}$

We know that the repulsive force that the charges exert is 6.4x10⁻¹N and that the distance between the charges is 3.8x10⁻¹⁰m.

Solve the equation above for q,

$q=\sqrt[]{\frac{F\cdot r^2}{k_e}}=r\sqrt[]{\frac{F}{k_e}}$

Replace with the values,

$q=3.8\cdot10^{-10}m\cdot\sqrt[]{\frac{6.4\cdot10^{-1}N}{8.988\cdot10^9N\cdot m^2/C^2}}$$q=3.8\cdot10^{-10}m\cdot\sqrt[]{7.12\cdot10^{-11}\frac{C^2}{m^2}}$$q=3.8\cdot10^{-10}m\cdot8.44\cdot10^{-6}\frac{C^{}}{m^{}}$$q=3.2\cdot10^{-15}C$

Each charge is 3.2 · 10⁻¹⁵ C