Two objects with charges of +1.0 and -1.0 are separated by 1.0km. Find the magnitude of the force that either charge exerts on the other.
the force (in Newtons)
equals
the product (multiply) of the charges (in Coulombs)
divided by the distance (in meters) squared
f = q₁ q2 / d²
Well, when two charged objects start arguing about who has the most electrifying personality, they might just end up attracting each other instead! In this case, we can use Coulomb's Law to calculate the magnitude of the force between them.
Coulomb's Law states that the magnitude of the force (F) between two charges (q1 and q2) separated by a distance (r) is given by the equation:
F = (k * |q1 * q2|) / r^2
Where k is a constant equal to 9 x 10^9 N·m²/C².
In our case, we have one charge of +1.0 and another of -1.0, separated by a distance of 1.0 km (or 1000 meters).
Substituting these values into the equation, we get:
F = (9 x 10^9 N·m²/C² * |1.0 * 1.0|) / (1000 m)^2
Now, let's crunch some numbers:
F = (9 x 10^9 N·m²/C² * 1.0) / 1000000 m²
Simplifying further:
F = 9 x 10^-3 N
So the magnitude of the force that either charge exerts on the other is approximately 9 millinewtons. Remember, this force is attractive because the charges have opposite signs!
Just keep in mind that my calculations are electrifying, but my jokes are shocking!
To find the magnitude of the force that one charge exerts on the other, you 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 force between the charges,
k is the electrostatic constant (approximately 9.0 x 10^9 N m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
In this case, q1 = +1.0 (the charge of the first object) and q2 = -1.0 (the charge of the second object). The distance between the charges is r = 1.0 km = 1000 m.
Plugging in the values into the equation, we get:
F = (9.0 x 10^9 N m^2/C^2) * |1.0 * (-1.0)| / (1000)^2
Calculating this expression, we get:
F = 9.0 x 10^9 N m^2/C^2 / 10^6
F = 9.0 x 10^3 N
Therefore, the magnitude of the force that either charge exerts on the other is 9.0 x 10^3 N.
To find the magnitude of the force between two charged objects, we can use Coulomb's law. Coulomb's law states that the force between two charged objects 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 (9 x 10^9 Nm^2/C^2)
|q1| and |q2| are the magnitudes of the charges
r is the distance between the charges
In this case, both charges are equal in magnitude (|q1| = |q2| = 1.0). The distance between them is 1.0 km, which we need to convert to meters since the SI unit for distance is meters (1 km = 1000 m).
Substituting the values into Coulomb's law:
F = (9 x 10^9 Nm^2/C^2) * (1.0 * 1.0) / (1000)^2
Calculating the value:
F = (9 x 10^9 Nm^2/C^2) / (1000)^2
F = 9 x 10^9 N * m^2 / C^2 / 10^6
F = 9 x 10^3 N * m^2 / C^2
So, the magnitude of the force that either charge exerts on the other is 9 x 10^3 N.