Respuesta :
Answer:
Charge, [tex]q=1.72\times 10^{-16}\ C[/tex]
Explanation:
It is given that, two tiny spheres have the same mass and carry charges of the same magnitude. Let charge on both sphere is q.
Also, the gravitational force that each sphere exerts on the other is balanced by the electric force i.e.
[tex]F_g=F_e[/tex]
[tex]G\dfrac{m^2}{r^2}=k\dfrac{q^2}{r^2}[/tex]
[tex]q=\sqrt{\dfrac{Gm^2}{k}}[/tex]
Where
G is the universal gravitational constant
k is the electrostatic constant
[tex]q=\sqrt{\dfrac{6.67\times 10^{-11}\ Nm^2/kg^2\times (2\times 10^{-6}\ kg)^2}{9\times 10^9\ Nm^2/C^2}}[/tex]
[tex]q=1.72\times 10^{-16}\ C[/tex]
So, the charge on both the spheres is [tex]1.72\times 10^{-16}\ C[/tex]. Hence, this is the required solution.
Answer:
[tex] q =5.439\times 10^{-17}C[/tex]
Explanation:
Given:
Mass of the tiny sphere, M = 2.0 × 10⁻⁶ kg
also masses are equal i.e M₁ = M₂
Now,
the gravitational force between the two masses M₁ and M₂ is given as:
[tex]F_G = \frac{GM_1M_2}{r^2}[/tex]
where,
G is the gravitational force constant = 6.67 x 10⁻¹¹ m³/kg.s²
r = center to center distance between the masses
also,
Electric force between the charges is given as
[tex]F_e=\frac{kq_1q_2}{r^2}[/tex]
where,
q₁ and q₂ are the charges and also it is given that q₁=q₂=q
k is the coulomb's law constant = 9.0 x 10⁹ N.m²/C²
since it is mentioned that [tex]F_G = F_e[/tex]
we have
[tex]\frac{kq_1q_2}{r^2} = \frac{GM_1M_2}{r^2}[/tex]
or
[tex]{9\times 10^9\times q^2} ={6.67\times 10^{-11}(2.0\times 10^{-6})^2}[/tex]
or
[tex] q =5.439\times 10^{-17}C[/tex]
