Question

wo tiny spheres have the same mass and carry charges of the same magnitude. The mass of each sphere is 2.0 × 10−6 kg. The gravitational force that each sphere exerts on the other is balanced by the electric force. determine the charge magnitude.

Answer 1

`q =5.439* 10^(-17)C`

Step-by-step 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:

`F_G = (GM_1M_2)/(r^2)`

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

`F_e=(kq_1q_2)/(r^2)`

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
`F_G = F_e`

we have

`(kq_1q_2)/(r^2) = (GM_1M_2)/(r^2)`

or

`{9* 10^9* q^2} ={6.67* 10^(-11)(2.0* 10^(-6))^2}`

or

`q =5.439* 10^(-17)C`

Answer 2

Charge,
`q=1.72* 10^(-16)\ C`

Step-by-step 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.

`F_g=F_e`

`G(m^2)/(r^2)=k(q^2)/(r^2)`

`q=\sqrt{(Gm^2)/(k)}`

Where

G is the universal gravitational constant

k is the electrostatic constant

`q=\sqrt{(6.67* 10^(-11)\ Nm^2/kg^2* (2* 10^(-6)\ kg)^2)/(9* 10^9\ Nm^2/C^2)}`

`q=1.72* 10^(-16)\ C`

So, the charge on both the spheres is
`1.72* 10^(-16)\ C`. Hence, this is the required solution.