Question

The force between a positively charged foam cup and a positively charged metal sphere is 5.2 × 10⁻⁴ newtons. The charge on the cup is 7.2 × 10⁻⁶ coulombs, and the charge on the metal sphere is 6.8 × 10⁻⁶ coulombs. What is the distance between the two objects? (k = 9.0 × 10⁹ newton·meters²/coulombs²)

Part A: Enter the variable symbol for the quantity you need to find. Use your keyboard and the keypad to enter your answer. Then click done.

Options:
A) r
B) q₁
C) q₂
D) F

Answer 1

To find the distance (r) between the positively charged foam cup and the metal sphere, we use Coulomb's law by rearranging it to solve for r. After plugging in the given values for the force, charges, and Coulomb's constant, the distance can be calculated.

Step-by-step explanation:

To calculate the distance between the positively charged foam cup and the positively charged metal sphere, we will use Coulomb's law, which is F = k * (|q₁ * q₂| / r²), where F is the force between the charges, k is Coulomb's constant, q₁ and q₂ are the charges on the objects, and r is the distance between the centers of the two charges.

In this case, the force (F) is given as 5.2 × 10⁻´ Newtons, the charge on the cup (q₁) is 7.2 × 10⁻⁶ Coulombs, the charge on the sphere (q₂) is 6.8 × 10⁻⁶ Coulombs, and Coulomb's constant (k) is 9.0 × 10⁹ N·m²/C².

The variable we are solving for is the distance r between the two objects. Thus, rearranging Coulomb's law to solve for r, we get r = √(k * |q₁ * q₂| / F). Plugging in the values:

r = √[(9.0 × 10⁹ N·m²/C²) * (|7.2 × 10⁻⁶ C * 6.8 × 10⁻⁶ C|) / (5.2 × 10⁻´ N)]

Now, calculate the value inside the square root and then take the square root to find the value of r, which will be the distance between the charged cup and sphere.