A-4.0 uC charge is located0.30m to the left of a +6.0 charge. What is the magnitude and the direction of the electrostatic force on the positive charge
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To find the magnitude and direction of the electrostatic force on the positive charge, we can use Coulomb's Law.
Coulomb's Law states that the electrostatic force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's denote the positive charge as Q1 (+6.0 μC) and the negative charge as Q2 (-4.0 μC).
Given:
Q1 = +6.0 μC
Q2 = -4.0 μC
Distance between the charges (r) = 0.30 m
First, let's find the magnitude of the electrostatic force using Coulomb's Law formula:
F = k * |Q1 * Q2| / r^2
where:
F is the magnitude of the electrostatic force between the charges,
k is the electrostatic constant (9.0 x 10^9 N⋅m^2/C^2),
|Q1 * Q2| is the absolute value of the product of the charges,
r^2 is the square of the distance between the charges.
Plugging in the values:
F = (9.0 x 10^9 N⋅m^2/C^2) * |(+6.0 μC) * (-4.0 μC)| / (0.30 m)^2
The absolute value of the product of the charges is |(+6.0 μC) * (-4.0 μC)| = 24.0 μC^2
F = (9.0 x 10^9 N⋅m^2/C^2) * (24.0 μC^2) / (0.30 m)^2
Calculating the magnitude of the electrostatic force:
F = 7.2 x 10^-3 N
Therefore, the magnitude of the electrostatic force on the positive charge is 7.2 x 10^-3 N.
To determine the direction of the force, we need to consider the signs of the charges.
Since the positive charge Q2 is to the left of the negative charge Q1, the electrostatic force will be attractive in nature, pulling Q2 towards Q1.
Hence, the direction of the electrostatic force on the positive charge is towards the right.
To calculate the magnitude and direction of the electrostatic force on the positive charge, we can use Coulomb's Law, which states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's break down the problem into steps:
Step 1: Define the given values
- Charge of the positive charge (q1) = +6.0 C
- Charge of the negative charge (q2) = -4.0 C
- Distance between the charges (r) = 0.30 m (to the left)
Step 2: Calculate the electrostatic force
Coulomb's Law formula is given by:
F = k * |q1 * q2| / r^2
Where:
- F = Electrostatic force between the charges
- k = Coulomb's constant (k = 8.99 x 10^9 N m^2/C^2)
- | | = Absolute value (to consider only the magnitude)
Plugging in the given values into the formula, we get:
F = (8.99 x 10^9 N m^2/C^2) * |6.0 C * (-4.0 C)| / (0.30 m)^2
Simplifying the calculation:
F = 8.99 x 10^9 N m^2/C^2 * 24.0 C^2 / 0.09 m^2
F = 8.99 x 10^9 N * 24.0 C^2 / 0.09 m^2
F = 8.99 x 24.0 / (0.09) N
F = 21595.555... N
Therefore, the magnitude of the electrostatic force on the positive charge is approximately 21595.56 N.
Step 3: Determine the direction
Since the positive charge is located to the right of the negative charge, the electrostatic force acts in the opposite direction (to the left).
Hence, the direction of the electrostatic force on the positive charge is to the left.
In summary, the magnitude of the electrostatic force on the positive charge is approximately 21595.56 N, and the direction of the force is to the left.