In Fig. 21-24, the particles have charges q1 = -q2 = 400 nC and q3 = -q4 = 92 nC, and distance a = 5.0 cm. What are the (a) x and (b) y components of the net electrostatic force on particle 3?

The figure cannot be uploaded, but the particles are located as a square, with q1 in the upper left, q2 in the upper right, q3 in the lower left, and q4 in the lower right.

F13=k•q1•q3/a² =

=9•10^9•400•10^-9•92•10^-9/25•10^-4=
=0.132 N
F13(x) =0, F13(y) =0.132 N
F43= k•q4•q3/a² =
=9•10^9•92•10^-9•92•10^-9/25•10^-4=
=0.0305 N
F43(x)= - 0.0305 N. F43(y)= 0
F23= k•q2•q3/(a√2)²= 9•10^9•400•10^-9•92•10^-9/1.41•25•10^-4=0.0936 N
F23 directed along the diagonal of the square (towards q2)
F23(x) =F23(y)=
=0.0936•cos 45=0.0936•0.707=0.0662 N.

F(x) = F13(x) +F43(x) +F23(x) =
=0 - 0.0305+ 0.0662= 0.0357 N,
F(y) = F13(y) +F43(y) +F23(y)= 0.132+0+0.0662 =0.1982 N.

This answers is wrong don't use please.

To find the x and y components of the net electrostatic force on particle 3, we need to calculate the individual forces between particle 3 and each of the other particles, and then add them up vectorially.

Let's calculate the x component first.

The x component of a force depends on the distance between the particles in the x direction, so we need to find the horizontal distance between each pair of particles.

In this case, since particle 1 is located in the upper left and particle 3 is located in the lower left, the horizontal distance between them is zero.

Similarly, the horizontal distance between particle 2 (located in the upper right) and particle 3 (located in the lower left) is also zero.

Now, let's calculate the force between particle 3 and particle 4.

The force between two charges can be calculated using Coulomb's law:

F = (k * |q1 * q2|) / r^2

Where:
- F is the force between the charges,
- k is the Coulomb constant (9 * 10^9 N m^2/C^2),
- q1 and q2 are the magnitudes of the charges,
- and r is the separation distance between the charges.

In this case, the charges are q3 and q4 with magnitudes |q3| = |q4| = 92 nC, and the separation distance between them is a = 5.0 cm = 0.05 m.

Calculating the force between particle 3 and particle 4:

F34 = (k * |q3 * q4|) / a^2

Plugging in the values:

F34 = (9 * 10^9 N m^2 / C^2) * (92 nC * 92 nC) / (0.05 m)^2

Calculating this will give you the magnitude of the force between particle 3 and particle 4.

Next, to find the x component, we need to multiply this magnitude by the cosine of the angle between the force and the x-axis. In this case, the angle between the force and the x-axis is 45 degrees because the forces between particle 3 and particles 1 and 2 cancel out in the x-direction.

So the x component of the net electrostatic force on particle 3 is:

Fx = F34 * cos(45°)

Now, let's move on to calculate the y component.

The y component of the net force depends on the distance between the particles in the y direction. Again, the vertical distance between particle 1 and particle 3 and between particle 2 and particle 3 is zero.

To find the y component of the force between particle 3 and particle 4, we multiply the magnitude of the force by the sine of the angle between the force and the y-axis. In this case, the angle between the force and the y-axis is also 45 degrees.

So the y component of the net electrostatic force on particle 3 is:

Fy = F34 * sin(45°)

Calculating these formulas will give you the x and y components of the net electrostatic force on particle 3.

To determine the (a) x and (b) y components of the net electrostatic force on particle 3, we can follow these steps:

Step 1: Calculate the electric force between q1 and q3.

Since q1 and q3 are opposite in charge, the force between them is attractive. The electric force between two charges is given by Coulomb's Law:

F₁₃ = (k * |q₁ * q₃|) / r₁₃²

Where:
F₁₃ is the force between q1 and q3,
k is Coulomb's constant (≈ 9 x 10^9 N•m²/C²),
q₁ and q₃ are the charges of particle 1 and particle 3, respectively,
|r₁₃| is the distance between the two charges.

In this case, the charges are q₁ = -400 nC and q₃ = -92 nC, and the distance is r₁₃ = a = 5.0 cm = 0.05 m.

Plugging in the values:

F₁₃ = (9 x 10^9 N•m²/C² * |-400 nC * -92 nC|) / (0.05 m)²

Note: The absolute value is used to ensure a positive force since Coulomb's Law only gives the magnitude of the force.

Step 2: Calculate the x and y components of F₁₃.

Since particles 1 and 3 are located diagonally opposite, the x-component of F₁₃ will be directed towards the right, and the y-component of F₁₃ will be directed upwards:

F₁₃x = F₁₃ * cos(45°)
F₁₃y = F₁₃ * sin(45°)

Step 3: Calculate the electric force between q2 and q3.

Since q2 and q3 are the same in charge, the force between them is repulsive. Therefore, F₂₃ will be directed towards the left.

In this case, the charges are q₂ = -q₄ = -92 nC, and the distance r₂₃ = a = 5.0 cm = 0.05 m.

Using Coulomb's Law:

F₂₃ = (9 x 10^9 N•m²/C² * |-92 nC * -92 nC|) / (0.05 m)²

Step 4: Calculate the x and y components of F₂₃.

Since particles 2 and 3 are located vertically opposite, the x-component of F₂₃ will be directed towards the left, and the y-component of F₂₃ will be zero since they are aligned along the y-axis.

F₂₃x = F₂₃
F₂₃y = 0

Step 5: Calculate the net x and y components of the force on particle 3.

The net force on particle 3 will be the vector sum of the forces F₁₃x and F₂₃x in the x-direction and the vector sum of F₁₃y and F₂₃y in the y-direction:

Net Fx = F₁₃x + F₂₃x
Net Fy = F₁₃y + F₂₃y

These values will give you the x and y components of the net electrostatic force on particle 3.