A charge q1=7.00 x 10^-6 is placed 0.300m from a second charge q2=-5x10^-6 C. Find the magnitude the force between the two charges.
A charge q1=7.00 x 10^-6 is placed 0.300m from a second charge q2=-5x10^-6 C. Find the magnitude the force between the two charges.
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To find the magnitude of the force between the two charges, you can use Coulomb's Law. Coulomb's Law states that the magnitude of the force, F, between two charges, q1 and q2, separated by a distance r, can be calculated using the formula:
F = (k * |q1 * q2|) / r^2
Where:
F is the magnitude of the force,
k is the electrostatic constant, approximately equal to 8.99 x 10^9 N m^2/C^2,
|q1 * q2| is the absolute value of the product of the two charges, and
r is the distance between the charges.
Given:
q1 = 7.00 x 10^-6 C,
q2 = -5 x 10^-6 C, and
r = 0.300 m.
Plugging in these values into the formula, we can calculate the magnitude of the force:
F = (8.99 x 10^9 N m^2/C^2 * |7.00 x 10^-6 C * -5 x 10^-6 C|) / (0.300 m)^2
Calculating the absolute value and simplifying:
F = (8.99 x 10^9 N m^2/C^2 * 7.00 x 10^-6 C * 5 x 10^-6 C) / (0.300 m)^2
F = (8.99 x 10^9 N m^2/C^2 * 35 x 10^-12 C^2) / 0.09 m^2
F = (314.65 x 10^-3 N m^2/C^2) / 0.09 m^2
F = 3496.111 N
Therefore, the magnitude of the force between the two charges is approximately 3496.111 N.
To find the magnitude of the force between two charges, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electrostatic force (F) between two point charges (q1 and q2) 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 magnitude of the force
k is the electrostatic constant (k = 8.99 x 10^9 N·m^2/C^2)
q1 and q2 are the charges of the two objects
r is the distance between the charges
In this case, we have:
q1 = 7.00 x 10^-6 C
q2 = -5 x 10^-6 C
r = 0.300 m
Plugging these values into the formula, we get:
F = (8.99 x 10^9 N·m^2/C^2) * |7.00 x 10^-6 C * (-5 x 10^-6 C)| / (0.300 m)^2
Calculating the absolute value of the charges and squaring the distance, we get:
F = (8.99 x 10^9 N·m^2/C^2) * (35 x 10^-12 C^2) / (0.09 m^2)
Simplifying the expression, we get:
F = (26.65 x 10^-3 N·m^2)/m^2
To convert the unit to newtons (N), we multiply by 1 N = 1 kg·m/s^2:
F = 26.65 x 10^-3 N
Finally, the magnitude of the force between the two charges is approximately 0.0267 N.