Three identical metal spheres are hung from a ceiling on rigid non-conducting rods. Sphere 1, sphere 2, and sphere 3 have charges
75 µC, −44 µC, and 50 µC, respectively. Each sphere is separated by
0.15 m.
What is the net electric force on the middle sphere due to spheres 1 and 3?
I think it's Coulomb's law:
F = kq1q2/r^2, but not sure.
Please explain in details so i understnad it. thanks
Yes, you are correct. The net electric force on the middle sphere can be determined using Coulomb's Law, which states that the electric 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 equation is:
F = k * (q1 * q2) / r^2
where:
F is the electric force
k is the electrostatic constant (approximately equal to 9 x 10^9 N·m^2/C^2)
q1 and q2 are the charges of the two objects
r is the distance between the centers of the spheres
In this case, we have three spheres. Sphere 1 and Sphere 3 are contributing to the net force on the middle sphere.
To calculate the net electric force on the middle sphere, we need to calculate the individual forces between the middle sphere and Sphere 1, as well as the individual forces between the middle sphere and Sphere 3. Once we have these individual forces, we can add them together to get the net force.
First, let's calculate the force between the middle sphere and Sphere 1:
F1 = k * (q1 * q2) / r^2
= (9 x 10^9 N·m^2/C^2) * [(75 x 10^-6 C) * (44 x 10^-6 C)] / (0.15 m)^2
Next, let's calculate the force between the middle sphere and Sphere 3:
F3 = k * (q1 * q3) / r^2
= (9 x 10^9 N·m^2/C^2) * [(75 x 10^-6 C) * (50 x 10^-6 C)] / (0.15 m)^2
Finally, we can find the net force by summing up the forces:
Net force = F1 + F3
Plug in the values and calculate each force to find the net electric force acting on the middle sphere due to Sphere 1 and Sphere 3.
Yes, you're correct. To find the net electric force on the middle sphere due to spheres 1 and 3, we can use Coulomb's law. Coulomb's law states that the force between two charged objects is proportional to the product of their charges and inversely proportional to the square of the distance between them:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the force between the charges,
k is the electrostatic constant, which has a value of 9 × 10^9 N m^2/C^2,
|q1| and |q2| are the magnitudes of the charges,
and r is the distance between the charges.
Let's calculate the force on the middle sphere due to sphere 1 first. The charge of sphere 1 is 75 µC, and the distance between sphere 1 and the middle sphere is 0.15 m. Plugging those values into Coulomb's law:
F1 = k * (|q1| * |q2|) / r^2 = (9 × 10^9 N m^2/C^2) * (75 × 10^(-6) C) * (50 × 10^(-6) C) / (0.15 m)^2
Now, let's calculate the force on the middle sphere due to sphere 3. The charge of sphere 3 is 50 µC, and the distance between sphere 3 and the middle sphere is also 0.15 m:
F3 = k * (|q1| * |q3|) / r^2 = (9 × 10^9 N m^2/C^2) * (75 × 10^(-6) C) * (50 × 10^(-6) C) / (0.15 m)^2
Finally, to find the net electric force on the middle sphere due to spheres 1 and 3, we need to add the forces together:
Net force = F1 + F3
Calculate F1, F3, and add them up to find the net force on the middle sphere.
yes, it is coulomb's law. I assume the charges are left to right, 1,2,3
well the force on 2 from one is to the right(it repulses).
the force on 2 from 3 is attractive, so it is to the right.
So, the easy way is to figure the magnitude of each force, then ADD them, and the resultant is tso the right.
You seem to have forgotten to read directions.
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