Determine the magnitude and direction of the total electric force on the +q charge by the +Q and -Q charges respectively. it should express and algebraic expression using Q,q,x,d and fundamental constants.


-- I am trying to post a graph but it is not willing to so I will try to explain it --

Q+ is up on the y access ( x = 0 ) and Q- is down the y access ( x = 0 ) , both at equal distances d of the origin. q is to the right of the x access ( y = 0 ) at a distance x from the origin

So I am trying to solve it like this
Net Force = (Force of +Q on q) + ( Force of -Q on q)

using this equation for force (Kq1q2)/r^2

but then we need to find the components right ?

so I thought it is like this

Fnet = sqrt ( Fnet of x components )^2 + (Fnet of y component)^2

but then for the x components , the r in the equation should be x ,, and for the y components the r should be d

am I right ? I feel confused and I think I am wrong :S

You are almost right, however, it is easier for me to break up the two forces into vertical and horizontal components.

well, first, the force on q from Q is kQq/distance^2 at some angle from the horizonal (arc tan d/x)
the horizontal force is
a) kqq/distanc^2*cosTheta
if you calculate the horizontal force component from -Q, it is the same but in a opposite direction, so the net horizontal force is ZERO.

Vertical forces:
vertical force from Q (top) is
kQq/distance^2 * sinTheta in the down direction
vertical force from -Q (bottom) is the same, and in the down direction.

so the net force is downward,

2kQq/(d^2+x^2) * sin (arctan d/x)

Thank you very much :D

You are on the right track in your approach to find the net force on the +q charge. Let's break down the calculations step-by-step:

1. Calculate the x-component of the forces:
The x-component of the force due to the +Q charge on the +q charge can be found using the equation: (KQq)/(r^2), where r is the distance between the +Q and +q charges.
So, the x-component of the force due to the +Q charge on the +q charge is: (KQq)/(x^2).

Similarly, the x-component of the force due to the -Q charge on the +q charge can be found using the same equation, but with a negative sign since it's acting in the opposite direction:
So, the x-component of the force due to the -Q charge on the +q charge is: -(KQq)/(x^2).

2. Calculate the y-component of the forces:
The y-component of the force due to the +Q charge on the +q charge can be found using the equation: (KQq)/(r^2), where r is the distance between the +Q and +q charges.
So, the y-component of the force due to the +Q charge on the +q charge is: (KQq)/(d^2).

Similarly, the y-component of the force due to the -Q charge on the +q charge can be found using the same equation, but with a negative sign since it's acting in the opposite direction:
So, the y-component of the force due to the -Q charge on the +q charge is: -(KQq)/(d^2).

3. Calculate the net force:
To find the magnitude of the net force, you can use the Pythagorean theorem:
Net force = sqrt[(x-component of force)^2 + (y-component of force)^2]

4. Determine the direction of the net force:
The direction of the net force can be found by calculating the angle it makes with the positive x-axis. You can use the inverse tangent (arctan) function to determine this angle:
Direction = arctan((y-component of force) / (x-component of force))

Remember to substitute the appropriate values for Q, q, x, d, and the fundamental constants (e.g., K for the electrostatic constant) in the equations.

I hope this helps! Let me know if you have any further questions.

To determine the magnitude and direction of the total electric force on the +q charge by the +Q and -Q charges, we can break down the problem into components and calculate each force separately.

Let's start by calculating the force of the +Q charge on the +q charge. The force between two charges is given by the equation:

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

where F is the force, k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

In this case, q1 is the charge on the +Q charge and q2 is the charge on the +q charge. The distance between them is x since they are along the x-axis. Hence, the force of the +Q charge on the +q charge is:

F1 = (k * Q * q) / x^2.

Now let's calculate the force of the -Q charge on the +q charge. Since the -Q charge is located along the y-axis and the +q charge is on the x-axis, we need to find the distance between them. Using the Pythagorean theorem, we have:

d^2 = x^2 + (2d)^2
d^2 = x^2 + 4d^2
d^2 - 4d^2 = x^2
-3d^2 = x^2
d^2 = -x^2 / 3
d = sqrt(-x^2 / 3).

The force between the -Q charge and the +q charge is given by:

F2 = (k * (-Q) * q) / d^2.

To calculate the net force on the +q charge, we need to add the forces together:

F_net = F1 + F2.

Now, let's determine the magnitude and direction of the net force. To find the magnitude, we use the equation you mentioned:

|F_net| = sqrt((F_net of x components)^2 + (F_net of y components)^2).

The x components of the forces F1 and F2 are F1_x = F1 * cos(θ1) and F2_x = F2 * cos(θ2), respectively, where θ1 and θ2 are the angles with respect to the x-axis.

The y components of the forces F1 and F2 are F1_y = F1 * sin(θ1) and F2_y = F2 * sin(θ2).

Finally, you can substitute the values and algebraically express the magnitude and direction of the total electric force using Q, q, x, d, and the fundamental constants.

Remember to consider the signs of the charges and the directions of the forces to correctly determine the direction of the net force.