Three point charges, +6.0 µC, +1.7 µC, and

−2.3 µC, lie along the x-axis at 0 cm, 1.7 cm,
and 6.0 cm, respectively.
What is the force exerted on q1 by the other
two charges? (To the right is positive.) The
Coulomb constant is 8.99 × 10
9
N · m2
/C
2
.
Answer in units of N

First, let's find the force exerted by q2 on q1:

F21 = (k * q1 * q2) / r21^2

where k is the Coulomb constant, q1 and q2 are the charge magnitudes, and r21 is the distance between them.

F21 = (8.99 * 10^9 N * m^2 / C^2) * (+6.0 * 10^-6 C) * (+1.7 * 10^-6 C) / (1.7 * 10^-2 m)^2
F21 = 3.69 N (to the right)

Now, let's find the force exerted by q3 on q1:

F31 = (k * q1 * q3) / r31^2

where r31 is the distance between q1 and q3.

F31 = (8.99 * 10^9 N * m^2 / C^2) * (+6.0 * 10^-6 C) * (-2.3 * 10^-6 C) / (6.0 * 10^-2 m)^2
F31 = -1.15 N (to the left)

The net force on q1 is the sum of these two forces:

F_net = F21 + F31
F_net = 3.69 N + (-1.15 N) = 2.54 N (to the right)

So the force exerted on q1 by the other two charges is 2.54 N (to the right).

To find the force exerted on q1 by the other two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The formula for calculating the force between two charges is:

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

Where:
F is the force between the charges,
k is the Coulomb constant (8.99 × 10^9 N · m^2 /C^2),
q1 and q2 are the charges,
and r is the distance between the charges.

In this case, we want to calculate the force exerted on q1 by the other two charges:

q1 = +6.0 µC
q2 = +1.7 µC
q3 = -2.3 µC

r1 = 1.7 cm (distance between q1 and q2)
r2 = 6.0 cm (distance between q1 and q3)

To calculate the force exerted on q1 by q2 and q3, we would calculate the forces between q1 and q2, and q1 and q3 separately, then add the forces together.

Force between q1 and q2:

F1 = k * |q1 * q2| / r1^2

Substituting the values:

F1 = (8.99 × 10^9 N · m^2 /C^2) * |(6.0 × 10^-6 C) * (1.7 × 10^-6 C)| / (0.017 m)^2

Calculating this, we get:

F1 = 2.45 N

Force between q1 and q3:

F2 = k * |q1 * q3| / r2^2

Substituting the values:

F2 = (8.99 × 10^9 N · m^2 /C^2) * |(6.0 × 10^-6 C) * (-2.3 × 10^-6 C)| / (0.060 m)^2

Calculating this, we get:

F2 = 1.35 N

Now, we can add the forces together to find the total force on q1:

Total force = F1 + F2

Substituting the calculated values:

Total force = 2.45 N + 1.35 N

Calculating this, we get:

Total force = 3.8 N

Therefore, the force exerted on q1 by the other two charges is 3.8 N.

To find the force exerted on q1 by the other two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

To calculate the force exerted on q1 by q2 and q3, we need to find the force between q1 and q2 and the force between q1 and q3 separately, and then add them up.

1. Force between q1 and q2:
We need to find the force exerted by q2 on q1. The formula for the force between two charges is given by:

F12 = (k * |q1 * q2|) / r^2

Where:
F12 is the force between q1 and q2,
k is the Coulomb constant (8.99 × 10^9 N · m^2 / C^2),
|q1 * q2| is the product of the magnitudes of the charges,
r is the distance between the charges.

In this case, q1 = +6.0 µC = 6.0 × 10^-6 C, q2 = +1.7 µC = 1.7 × 10^-6 C, and r12 = 1.7 cm = 1.7 × 10^-2 m.

Plugging in these values into the formula, we can calculate the force between q1 and q2:

F12 = (8.99 × 10^9 N · m^2 / C^2) * |(6.0 × 10^-6 C) * (1.7 × 10^-6 C)| / (1.7 × 10^-2 m)^2

2. Force between q1 and q3:
We need to find the force exerted by q3 on q1. Using the same formula as above, but now with q3 and r13, we can calculate the force:

F13 = (k * |q1 * q3|) / r^2

In this case, q1 = +6.0 µC = 6.0 × 10^-6 C, q3 = -2.3 µC = -2.3 × 10^-6 C, and r13 = 6.0 cm = 6.0 × 10^-2 m.

Plugging in these values into the formula, we can calculate the force between q1 and q3:

F13 = (8.99 × 10^9 N · m^2 / C^2) * |(6.0 × 10^-6 C) * (-2.3 × 10^-6 C)| / (6.0 × 10^-2 m)^2

3. Adding the forces:
Now, we can simply add the forces F12 and F13 to get the total force exerted on q1 by q2 and q3.

FTotal = F12 + F13

Calculating the total force will give us the answer in units of Newtons (N).