Three charges are fixed to an x, y coordinate system. A charge of +20 µC is on the y axis at y = 2.7 m. A charge of -14 µC is at the origin. Last, a charge of +46 µC is on the x axis at x = +2.7 m. Determine the magnitude and direction of the net electrostatic force on the charge at x = +2.7 m. Specify the direction relative to the −x axis.

First,find the force from each of the other charges:

Force at-45 degrees: k20*46*E-12/(2.7)^2

Force at 180 degrees: k20*14E-12/2.7^2

now break up the first force into -y,x components:
force in 0 deg (x): 20k*46E-12/2.7^2 *.707

force in -y : k20*46E-12/(2.7^2) * .707

net force in x direction:
k20*46/2.7^2 (.707-14/20)=zero check that.

Net force then is in -y direction, as given above.

wow lol XD

what is the net electrostatic force on the charge q3 -48ìc due to charges q1 (+78µC) and q2 (+50µC)

A point charge of +5µC is on the axis at y = 3cm, and a second point charge of -6µC is on the axis at y = -3cm. Where a third charge of +2µC should be placed so that the system is in equilibrium?

To determine the net electrostatic force on the charge at x = +2.7 m, we need to calculate the electrostatic force exerted by each of the other two charges and then find the vector sum of these forces.

The formula to calculate the electrostatic force between two point charges is given by Coulomb's Law:

F = (k*q₁*q₂)/r²

where F is the magnitude of the electrostatic force, k is Coulomb's constant (9 * 10^9 N*m²/C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between them.

We can break down the problem into two steps:

Step 1: Calculate the electrostatic force between the charge at x = +2.7 m and the charge on the y-axis.

The distance between these two charges is the distance along the x-axis, which is also 2.7 m. The magnitude of the electrostatic force can be calculated as:

F₁ = (k*q₁*q₂)/(r₁)²

Substituting the values:

F₁ = (9 * 10^9 N*m²/C²) * (20 * 10^-6 C) * (-14 * 10^-6 C) / (2.7 m)²

Calculate this expression to find the magnitude of F₁.

Step 2: Calculate the electrostatic force between the charge at x = +2.7 m and the charge at the origin.

The distance between these two charges is the distance along the x-axis, which is also 2.7 m. The magnitude of the electrostatic force can be calculated as:

F₂ = (k*q₁*q₂)/(r₂)²

Substituting the values:

F₂ = (9 * 10^9 N*m²/C²) * (46 * 10^-6 C) * (-14 * 10^-6 C) / (2.7 m)²

Calculate this expression to find the magnitude of F₂.

Now, we have the magnitude of the electrostatic forces F₁ and F₂. To find the net electrostatic force, we need to find the vector sum of these two forces. Since the charges are on the x-axis, the only component of the force that matters is the x-component. You can find the x-component of each force by multiplying its magnitude by the cosine of the angle between the force and the x-axis.

Finally, take the sum of these x-components to find the net electrostatic force.