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

3.2 · 10⁻¹⁵ C

Step-by-step explanation

By Coulomb's law,

`F=k_e\cdot(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(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[]{(F\cdot r^2)/(k_e)}=r\sqrt[]{(F)/(k_e)}`

Replace with the values,

`q=3.8\cdot10^(-10)m\cdot\sqrt[]{(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)(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