A charge of 7.1 x 10-4 C is placed at the origin of a Cartesian coordinate system. A second charge of 6.5 x 10-4 C lies 20 cm above the origin, and a third charge of 8.9 x 10-4 C lies 20 cm to the right of the origin. Determine the direction of the total force on the first charge at the origin. Express your answer as a positive angle in degrees measured counter clockwise from the positive x-axis.

α = 36.21 °

β = 143.79°

Explanation:

To do this, we need to know the expression to calculate the angle.

In this case:

α₁ = tan⁻¹ (Fy₁/Fx₁)   (1)

Now, let's analize the given data.

We have a charge q₁ at the origin of the cartesian coordinate system, so, it's at the 0. The charge q₂ is 20 cm above q₁, meaning is on the y-axis. Finally q₃ it's 20 cm to the right, meaning it's on the x-axis.

Knowing this,we can calculate the force that q₂ and q₃ are exerting over q₁. As these forces are in the x and y-axis respectively, we also are calculating the value of the forces in the x and y axis, that are needed to calculate the direction.

The expression to calculate the force would be Coulomb's law so:

F = K q₁q₂ / r²    (2)

The value of K is 9x10⁹ N m² / C². Let's calculate the forces:

F₁₂ = Fy = 9x10⁹ * (7.1x10⁻⁴) * (6.5x10⁻⁴) / (0.020)²

Fy = 1.04x10⁷ N

F₁₃ = Fx = 9x10⁹ * (7.1x10⁻⁴) * (8.9x10⁻⁴) / (0.020)²

Fx = 1.42x10⁷ N

Now that we have both forces, we can calculate the magnitude of the force:

F = √(Fx)² + (Fy)²

F = √(1.04x10⁷)² + (1.42x10⁷)²

F = 1.76x10⁷ N

Finally, the direction would be applying (1):

α = tan⁻¹ (1.04x10⁷/1.42x10⁷)

α = 36.21 °

And counter clockwise it would be:

β = 180 - 36.21 = 143.79°

Hope this helps

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.

well clustered together.

points close on a scatter diagram