In a thundercloud there may be an electric charge of 60 C near the top of the cloud and −60 C near the bottom of the cloud.
If these charges are separated by about 3 km, what is the magnitude of the elec- tric force between these two sets of charges? The value of the electric force constant is 8.98755 × 109 N · m2/C2.
Answer in units of N.
well I call it k = 9 * 10^9 so I can remember it :)
F = k Q1 Q2 /(d*d)
F = 9 * 10^9 * 60 * -60 / 9*10^6
= -3600 * 10^3 = -3.6 * 10^6 Newtons (Yikes! )
the direction is toward each other, like charges repel, unlike attract
thank you!!
To calculate the magnitude of the electric force between these two sets of charges, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric force between two point charges is given by the equation:
F = (k * |q1 * q2|) / r^2
where:
- F is the magnitude of the electric force
- k is the electric force constant (8.98755 × 10^9 N · m^2/C^2)
- q1 and q2 are the magnitudes of the charges (60 C and -60 C)
- r is the distance between the charges (3 km, which we need to convert to meters)
First, let's convert 3 km to meters:
3 km = 3,000 meters
Now, let's plug in the values into the equation:
F = (8.98755 × 10^9 N · m^2/C^2 * |60 C * (-60 C)|) / (3,000 meters)^2
Simplifying:
F = (8.98755 × 10^9 N · m^2/C^2 * 60 C * 60 C) / (3,000 meters)^2
F = (8.98755 × 10^9 N · m^2/C^2 * 3,600 C^2) / 9,000,000 meters^2
F = (32,353,800,000 N · m^2/C^2) / 9,000,000 meters^2
F ≈ 3594.87 N
Therefore, the magnitude of the electric force between these two sets of charges is approximately 3594.87 N.
To find the magnitude of the electric force between the charges, we can use Coulomb's Law, which states that the magnitude of the electric force between two charges is given by:
F = k * (|q1| * |q2|) / r^2
Where F is the magnitude of the electric force, k is the electric force constant (8.98755 × 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, the magnitude of the first charge is |q1| = 60 C, and the magnitude of the second charge is |q2| = 60 C. The distance between the charges is r = 3 km = 3000 m.
Substituting these values into the equation, we get:
F = (8.98755 × 10^9 N · m^2/C^2) * ((60 C) * (60 C)) / (3000 m)^2
Simplifying further,
F = (8.98755 × 10^9 N · m^2/C^2) * (3600 C^2) / (9000000 m^2)
F = (8.98755 × 10^9 N · m^2/C^2) * 0.0004
F = 3591020 N
Therefore, the magnitude of the electric force between the charges is 3,591,020 N.