A small charged sphere,A, carries 4 times the charge of another sphere B. When these are placed 4.5 cm apart, they experience a force of 0.016N attraction between them. Find the charge on B.
To find the charge on sphere B, we can use Coulomb's Law, which states that the force of attraction or repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between their centers.
Let's denote the charge on sphere B as q B .
We are given the following information:
- Charge on sphere A is 4 times the charge on sphere B (q A = 4q B ).
- The distance between the centers of the two spheres is 4.5 cm = 0.045 m.
- The force of attraction between the spheres is 0.016 N.
Using Coulomb's Law, we can write the equation:
F = k * (|q A | * |q B |) / r^2
where F is the force of attraction, |q A | and |q B | are the magnitudes of the charges on A and B respectively, r is the distance between their centers, and k is the electrostatic constant (k = 9 × 10^9 N m^2/C^2).
Substituting the given values:
0.016 = (9 × 10^9) * (|4q B | * |q B |) / (0.045^2)
Simplifying, we get:
0.016 = (9 × 10^9) * (16 q B^2) / (0.045^2)
Now, divide both sides of the equation by (9 × 10^9) * (16 / (0.045^2)) to solve for q B :
q B^2 = 0.016 * (0.045^2) / (9 × 10^9) * (16)
q B^2 = 0.01 × 0.045^2 / (9 × 16 × 10^9)
q B^2 = 0.01 × 0.002025 / 144 × 10^9
q B^2 = 0.00002025 / 144 × 10^9
q B^2 = 1.406(6.25 × 10^-13)
q B^2 = 8.84 × 10^-13
Taking the square root of both sides, we find:
q B = √8.84 × 10^-13
q B ≈ 2.973 × 10^-7 C
Therefore, the charge on sphere B is approximately 2.973 × 10^-7 Coulombs.