Question

Two identical particles each of mass M and charge Q are placed a certain distance apart. If they are in equilibrium

under mutual gravitational and electric force then calculate the order of Q/M in SI units.

Answer 1

Q / m = 8.61 10⁻¹¹ C / kg

Step-by-step explanation:

For this exercise we use the gravitational force of attraction

`F_g = G (m_1m_2)/(r^2)`

the electric force

`F_e = k (q1q2)/(r^2)`

indicate that the two forces are equal

G m₁ m₂ / r² = k q₁ q₂ / r²

they also say that the two masses are equal and the two charges are equal

G m² = k Q²

Q / m =
`\sqrt{(G)/(k) }`

we calculate

Q / m =
`\sqrt{(6.67 \ 10^(-11) )/(8.99 \ 10^9) }`

Q / m =
`\sqrt{ 0.7419 \ 10 ^(-20)}`

Q / m = 0.861 10⁻¹⁰

Q / m = 8.61 10⁻¹¹ C / kg