A charge of +80 mC is placed on the x axis at x = 0. A second charge of -50 mC is placed on the x axis at x = 50 cm. What is the magnitude of the electrostatic force on a third charge of 4.0 mC placed on the x axis at x = 30 cm?
pushed right by the first, sucked right by the second
F = k (4*10^-3) [ 80*10^-3 / 0.3^2 + 50^-3 / 0.5^2 ]
F = k (4*10^-3) [ 80*10^-3 / 0.3^2 + 50^-3 / 0.2^2 ]
To calculate the magnitude of the electrostatic force on the third charge, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = k * |q1 * q2| / r^2
Where:
- F is the electrostatic force between the charges
- k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2)
- q1 and q2 are the charges
- r is the distance between the charges
Let's calculate the electrostatic force using this formula.
First, let's convert the distances to meters:
- x1 = 0
- x2 = 50 cm = 0.5 m
- x3 = 30 cm = 0.3 m
Now, let's plug in the values into the formula:
F = (9 x 10^9 Nm^2/C^2) * |q1 * q3| / r^2
F = (9 x 10^9 Nm^2/C^2) * |(+80 x 10^-3 C) * (-4 x 10^-3 C)| / (0.5 m - 0.3 m)^2
F = (9 x 10^9 Nm^2/C^2) * (80 x 10^-3 C) * (4 x 10^-3 C) / (0.2 m)^2
F = (9 x 10^9 Nm^2/C^2) * (3.2 x 10^-6 C^2) / (0.2 m)^2
F = (9 x 10^9 Nm^2/C^2) * 3.2 x 10^-6 C^2 / 0.04 m^2
F = (9 x 10^9 Nm^2/C^2) * 0.08 x 10^-2
F = 72 N
Therefore, the magnitude of the electrostatic force on the third charge is 72 N.
To find the magnitude of the electrostatic force on the third charge, we can use Coulomb's law. Coulomb's law states that the magnitude of the electrostatic force between two charged objects is given by the equation:
F = (k * |q1 * q2|) / r^2
Where:
F is the magnitude of the electrostatic force,
k is Coulomb's constant (k = 8.99 * 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
In this case, the first charge q1 is +80 mC, the second charge q2 is -50 mC, and the distance r between them is 50 cm (or 0.5 m). We need to find the magnitude of the electrostatic force on the third charge, so q2 will be the charge of the third charge, which is 4.0 mC, and the distance r will be 30 cm (or 0.3 m).
Now we can plug in the values into the Coulomb's law equation:
F = (k * |q1 * q2|) / r^2
F = (8.99 * 10^9 Nm^2/C^2 * |80 * 10^(-3) C * 4.0 * 10^(-3) C|) / (0.3 m)^2
F = (8.99 * 10^9 Nm^2/C^2 * 320 * 10^(-6) C^2) / 0.09 m^2
F = (287.68 * 10^3 Nm^2) / 0.09 m^2
F = 3.19 * 10^6 N
Therefore, the magnitude of the electrostatic force on the third charge is 3.19 * 10^6 N.