two point charges are located on the y axis as follows :
charge q1 = -1.50nc at y= -0.600m, and
charge q2 = +3.2nc at the origin (y=0)
what is the net force (magnitude and direction) exerted by these two charges on a third charge q3 = +5.00 nc located at y = -0.400 m ?
The answer is
B: E
To find the net force exerted by the two charges on the third charge, we need to calculate the individual forces exerted by each charge and then add them vectorially.
Let's calculate the force exerted by q1 on q3 first:
1. Determine the distance between q1 and q3:
Distance between q1 and q3 = y3 - y1
Distance = (-0.400 m) - (-0.600 m)
= -0.400 m + 0.600 m
= 0.200 m
2. Calculate the magnitude of the force (F1) using Coulomb's Law:
F1 = (k * |q1| * |q3|) / (distance^2)
where k is the electrostatic constant with a value of 8.99 x 10^9 N m^2/C^2,
|q1| is the absolute value of q1,
|q3| is the absolute value of q3,
and distance is the distance between q1 and q3.
F1 = (8.99 x 10^9 N m^2/C^2 * |(-1.50 nC)| * |+5.00 nC|) / (0.200 m)^2
Using the absolute values for charge magnitudes:
F1 = (8.99 x 10^9 N m^2/C^2 * 1.50 x 10^-9 C * 5.00 x 10^-9 C) / (0.200 m)^2
F1 = (8.99 x 1.50 x 5.00) / 0.200^2 N
F1 = (67.425) / 0.040 N
F1 = 1685.625 N
So, the force exerted by q1 on q3 is 1685.625 N in the negative y-direction.
Now let's calculate the force exerted by q2 on q3:
1. Determine the distance between q2 and q3:
Distance between q2 and q3 = y2 - y3
Distance = 0.000 m - (-0.400 m)
= 0.400 m
2. Calculate the magnitude of the force (F2) using Coulomb's Law:
F2 = (k * |q2| * |q3|) / (distance^2)
F2 = (8.99 x 10^9 N m^2/C^2 * |(+3.20 nC)| * |+5.00 nC|) / (0.400 m)^2
F2 = (8.99 x 10^9 N m^2/C^2 * 3.20 x 10^-9 C * 5.00 x 10^-9 C) / (0.400 m)^2
F2 = (8.99 x 3.20 x 5.00) / 0.400^2 N
F2 = (143.2) / 0.160 N
F2 = 895 N
So, the force exerted by q2 on q3 is 895 N in the positive y-direction.
To find the net force, we need to add the individual forces as vectors:
Net Force = F1 + F2
Since the forces are in opposite directions, we need to subtract their magnitudes:
Net Force = |F1| - |F2|
Net Force = 1685.625 N - 895 N
Net Force = 790.625 N
Therefore, the net force exerted by these two charges on q3 is 790.625 N in the negative y-direction.
To find the net force exerted by the two charges on the third charge, you can use Coulomb's law, which states that the magnitude of the force between two charged objects is proportional to the product of their charges and inversely proportional to the square of the distance between them. Here's how to calculate it step by step:
1. Determine the distance between the first charge (q1) and the third charge (q3):
- The y-coordinate of q1 is -0.600 m, and the y-coordinate of q3 is -0.400 m, so the distance between them is |(-0.600) - (-0.400)| = 0.200 m.
2. Calculate the force exerted by q1 on q3:
- Use Coulomb's law formula: F = (k * |q1 * q3|) / r^2, where k is the electrostatic constant (k ≈ 9 x 10^9 Nm^2/C^2), q1 and q3 are the charges, and r is the distance between them.
- Substituting the values: F1 = (9 x 10^9 Nm^2/C^2) * |-1.50 x 10^-9 C * 5.00 x 10^-9 C| / (0.200 m)^2
3. Determine the distance between the second charge (q2) and the third charge (q3):
- q2 is located at the origin, so the distance between q2 and q3 is the y-coordinate of q3, which is 0.400 m.
4. Calculate the force exerted by q2 on q3:
- Substituting the values: F2 = (9 x 10^9 Nm^2/C^2) * |3.2 x 10^-9 C * 5.00 x 10^-9 C| / (0.400 m)^2
5. Find the net force:
- The net force is the vector sum of the forces exerted by q1 and q2. Since they are in opposite directions along the y-axis, you subtract their magnitudes to calculate the net force:
- Net force, F_net = |F1| - |F2|
Now that we have the equations, let's plug in the values and calculate the net force:
F1 = (9 x 10^9 Nm^2/C^2) * |-1.50 x 10^-9 C * 5.00 x 10^-9 C| / (0.200 m)^2
F2 = (9 x 10^9 Nm^2/C^2) * |3.20 x 10^-9 C * 5.00 x 10^-9 C| / (0.400 m)^2
F_net = |F1| - |F2|
Once you calculate these values, the magnitude of the net force (F_net) will give you the answer to the question, and its direction will be along the y-axis.