What is the net force exerted by these two charges on a third charge q 3 = 45.0nC placed between q 1 and q 2 at x 3 = -1.145m ?

Your answer may be positive or negative, depending on the direction of the force.

Express your answer numerically in newtons to three significant figures.

Coulomb's law for the magnitude of the force F between two particles with charges Q and Q �Œ separated by a distance d is

|F|=K|QQ �Œ | d 2 ,

where K=1 4ƒÎϵ 0 , and ϵ 0 =8.854�~10 −12 C 2 /(N⋅m 2 ) is the permittivity of free space.

Consider two point charges located on the x axis: one charge, q 1 = -14.5nC , is located at x 1 = -1.715m ; the second charge, q 2 = 32.5nC , is at the origin (x=0.0000) .

To calculate the net force exerted by the two charges on the third charge, we can use Coulomb's law. Coulomb's law states that the magnitude of the force between two charges is given by the equation:

|F| = K |q1q2| / d^2

Where:
- |F| is the magnitude of the force
- K is Coulomb's constant, equal to 1 / (4πϵ0), where ϵ0 is the permittivity of free space (8.854 × 10^-12 C^2 /(N∙m^2))
- q1 and q2 are the charges of the two charges
- d is the distance between the charges

In this case, we have q1 = -14.5nC, q2 = 32.5nC, and the distance between them is d = x3 = -1.145m.

First, let's calculate the magnitude of the force between q1 and q3:
|F1| = K |q1q3| / d1^2

Next, let's calculate the magnitude of the force between q2 and q3:
|F2| = K |q2q3| / d2^2

Finally, the net force exerted by the two charges on q3 is given by the vector sum of these two forces:

|Net Force| = |F1| + |F2|

Now, let's plug in the values and calculate:

K = 1 / (4πϵ0) = 9 × 10^9 N∙m^2 / C^2

|F1| = (9 × 10^9 N∙m^2 / C^2) × |-14.5nC × 45.0nC| / (-1.715m - (-1.145m))^2

|F2| = (9 × 10^9 N∙m^2 / C^2) × |32.5nC × 45.0nC| / (-1.145m - 0.0000m)^2

|Net Force| = |F1| + |F2|

Once you calculate the values for |F1|, |F2|, and |Net Force| using the above formulas and units, round your answer to three significant figures and express it numerically in newtons. The answer may be positive or negative depending on the direction of the force.