Three negatively charged sphere, each with a charge of a 4*10^-6C, are fixed at the vertices of an equilateral triangle whose sides are 20cm long. Calculate size and direction of the net electric force on each sphere.
Calculate the force between any two.
Now, look at any vertice. THe forces from adjacent corners are vectors, at 60 deg apart. The force componsnts away from the triangle add, and the force oomponents close to the corners are equal and opposite.
So I see twice the away component.
force away= 2*forcecoulomb*cos30
where force coulomb is the force between any two charges apart .2 m.
sketch it, check my thinking.
To calculate the net electric force on each sphere, we need to calculate the force between each pair of spheres and then sum them up vectorially.
Step 1: Calculate the force between two spheres.
The electric force between two charged spheres can be calculated using Coulomb's Law:
F = k * (|q1| * |q2|)/r^2
Where:
F is the magnitude of the force between the spheres,
k is the electrostatic constant, which is approximately equal to 9 x 10^9 N m^2/C^2,
|q1| and |q2| are the magnitudes of the charges on the spheres,
r is the distance between the centers of the spheres.
In this case, since all the spheres have the same charge magnitude, |q1| = |q2| = |q| = 4 * 10^-6 C. The distance between their centers, r, is equal to the length of one side of the equilateral triangle, which is 20 cm or 0.2 m.
So, the force between two spheres is:
F = (9 x 10^9 N m^2/C^2) * (4 * 10^-6 C)^2 / (0.2 m)^2
Now, we can calculate the magnitude and direction of the net electric force on each sphere.
Step 2: Calculate the net electric force on each sphere.
Since all three spheres have the same charge, the net force due to spheres 2 and 3 on sphere 1 will be equal in magnitude but opposite in direction to the net force due to spheres 1 and 3 on sphere 2 and so on.
Using vector addition, we can determine the net force on each sphere. By setting up a coordinate system with one sphere at the origin and the side of the equilateral triangle along the x-axis, and noting that the net force on each sphere will act along the line joining the centers of the spheres, we can find the resultant force on each sphere.
The magnitude and direction of the net electric force on each sphere can be calculated using the law of cosines and the law of sines.
Let's denote the magnitude of the net electric force on each sphere as F_net.
For sphere 1:
F_net = 2 * F * cos(60°)
For sphere 2:
F_net = 2 * F * cos(60°)
For sphere 3:
F_net = 2 * F * cos(0°)
Here, cos(60°) = 0.5 and cos(0°) = 1.
Now, you can substitute the value of F calculated in step 1 to find the magnitude and direction of the net electric force on each sphere.