Question

Two point charges (q_1) and (q_2) are (3.00 , {m}) apart, and their total charge is (20 , mu C).

a) If the force of repulsion between them is (0.075 , {N}), what are the magnitudes of the two charges?
A) (15 , mu C) and (5 , mu C)
B) (10 , mu C) and (10 , mu C)
C) (5 , mu C) and (15 , mu C)
D) (12 , mu C) and (8 , mu C)

Answer 1

The force of repulsion between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Given the total charge is 20 μC, and the force is 0.075 N, the charges are distributed in a way that q1 is smaller than q2, leading to (5 μC) and (15 μC) for a repulsive force. Therefore, the correct answer is C) (5 μC) and (15 μC).

Step-by-step explanation:

The force between two point charges
`\( F \)` is given by Coulomb's Law:

`\[ F = \frac{k \cdot }{{r^2}} \]`

where
`\( k \)` is Coulomb's constant
`(\( 8.99 * 10^9 \, N \cdot m^2/C^2 \)), \( q_1 \) and \( q_2 \)` are the magnitudes of the charges, and
`\( r \)` is the separation distance. The total charge is the sum of
`\( q_1 \) and \( q_2 \), so \( q_1 + q_2 = 20 \, \mu C \).`

Given
`\( F = 0.075 \, N \)` and
`\( r = 3.00 \, m \)`, we can set up the equation:

`\[ 0.075 = \frac{q_1 \cdot q_2}{{(3.00)^2}} \]`

Solving for
`\( |q_1 \cdot q_2| \)` gives
`\( |q_1 \cdot q_2| = 6.75 * 10^(-7) \, C^2 \).`

Now, since
`\( q_1 + q_2 = 20 \, \mu C \)`, we have a system of equations. Solving these equations, we find that
`\( q_1 = 5 \, \mu C \)` and
`\( q_2 = 15 \, \mu C \)`. This distribution of charges satisfies both the conditions of the problem and is consistent with the repulsive force observed at the given distance.

Therefore, the correct answer is C) (5 μC) and (15 μC).

Answer 2

Using Coulomb's Law, the equation for the force between two charges lets us solve for the magnitudes of the two charges that are 3.00 m apart and together have a total charge of 20 µC, which repel each other with a force of 0.075 N. The correct answer is D) (12 , mu C) and (8 , mu C).

Step-by-step explanation:

When dealing with the repulsion between two point charges, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

For two point charges q1 and q2 that are 3.00 m apart with a total charge of 20 μC, and a force of repulsion of 0.075 N, we can set up an equation based on Coulomb's Law to find the magnitudes of the charges.

Let q1 be the first charge and q2 = 20 μC - q1 be the second charge.

The force of repulsion is given by F = k * |q1 * q2| / r2, where k is Coulomb's constant, r is the distance between charges, q1 and q2 are the charges, and F is the force between them.

We can solve this equation to find the values of q1 and q2, which will either be split as 15 μC and 5 μC or as equal charges of 10 μC each, depending on the quadratic solution.

Therefore, the correct answer is D) (12 , mu C) and (8 , mu C).