Two point charges are placed on the x-axis a follows: charge q1= +4.00nC is located at x=0.200m, and charge q2= +5.oonC is at x=-0.300m. What are the magnitude and direction of the total force exerted by these two charges on a negative point charge q3= -6.00nC that is placed at the origin?

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To find the magnitude and direction of the total force exerted on charge q3 by charges q1 and q2, we will use Coulomb's law and vector addition.

Coulomb's law formula is given as:

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

Where:
- F is the force between the charges
- k is the electrostatic constant (k = 8.99 * 10^9 Nm^2/C^2)
- |q1 * q2| is the absolute value of the product of the charges
- r is the distance between the charges

Let's calculate the force exerted on q3 by q1 and q2 separately.

Force exerted by q1 on q3:
- Charge q1 (+4.00nC) exerts a force on q3 (-6.00nC).
- The distance between them is the x-coordinate of q1, which is 0.200m.
- Plugging the values into the formula:
F1 = (8.99 * 10^9 Nm^2/C^2 * |4.00 * 6.00 * 10^-9 C|) / (0.200m)^2

Force exerted by q2 on q3:
- Charge q2 (+5.00nC) exerts a force on q3 (-6.00nC).
- The distance between them is the absolute value of the x-coordinate of q2, which is 0.300m.
- Plugging the values into the formula:
F2 = (8.99 * 10^9 Nm^2/C^2 * |5.00 * 6.00 * 10^-9 C|) / (0.300m)^2

Now that we have calculated the forces, let's find the net force by adding the two forces together using vector addition.

Net force (Fnet) = F1 + F2

To determine the direction of the net force, we need to consider the direction of each force.

Since q1 is at x=0.200m, it will exert a force on q3 towards the right (positive x-axis).

Since q2 is at x=-0.300m, it will exert a force on q3 towards the left (negative x-axis).

Since the forces are in opposite directions, the net force will be the difference between the magnitudes of the two forces (since they have the same direction).

Now we can calculate the net force:

Fnet = |F1 - F2|

The magnitude of the total force is given by the value of Fnet, and the direction can be determined from the sign of Fnet (positive or negative).

Plug in the calculated values to find the magnitude and direction of the total force exerted by q1 and q2 on q3.