A small glass bead has been charged to + 30 nC . A tiny ball bearing 1.0 cm above the bead feels a 1.8×10^−2 N downward electric force. What is the charge on the ball bearing?

Respuesta :

Answer:

The charge on the ball bearing = 667 nC or 6.67 × 10⁻⁷ C

Explanation:

Coulombs law: The force of attraction or repulsion between two charges, Q₁ and Q₂, is directly proportional to the product of the charges and inversely proportional to the square of the distance between the two charges

From coulombs law, F =1/4πε₀ (Q₁Q₂/r²) ............. Equation 1

making Q₂ the subject of the equation,

Q₂ =( F×r²)/(Q₁×1/4πε₀) ..................... Equation 2

Where F = force of attraction, Q₁ = charge of the bead, Q₂ = charge of the ball bearing, r = distance between the bead and the ball bearing.

Given: Q₁ = 30 nC = 30×10⁻⁹ C,  F = 1.8×10⁻² N,

             r = 1.0 cm = (1/100) = 0.01 m

Constant: 1/4πε₀ = 9×10⁹ Nm²/C²

Substituting these values intto equation 2,

Q₂ = [(1.8×10⁻²)(0.01)²]/[(9×10⁹)(30×10⁻⁹)]

Q₂ = (1.8×10⁻² × 0.0001)/270

Q₂ = 6.67 × 10⁻⁷ C. = 667 nC

Therefore the charge on the ball bearing = 667 nC

The force of attraction or repulsion between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of distance between them.

The charge on the ball bearing is 667 nC.

What is coulombs law?

Coulombs law states the the force of attraction or repulsion between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of distance between them.

It can be given as,

[tex]F=k\dfrac{q_1\times q_2}{r^2}[/tex]

Here, [tex]k[/tex] is coulombs constant.

Given information-

The charge on the small glass bead is + 30 nC.

The diameter of the ball bearing is 1.0 cm.

The bead feels the electric force due to ball bearing is 1.8×10^−2 N downward .

Let [tex]q[/tex] is the charge on the ball bearing. Thus, put the values in the above formula as,

[tex]1.8\times10^{-2}=8.988\times10^{9}\times\dfrac{10\times10^{-9}\times q}{0.01^2}\\q=6.67\times10^[-7]\rm C\\q=667\rm nC\\[/tex]

Hence the charge on the ball bearing is 667 nC.

Learn more about the coulombs law here;

https://brainly.com/question/506926

RELAXING NOICE
Relax