Three point charges, +6.5 ¦ÌC, +1.4 ¦ÌC, and
−3.9 ¦ÌC, lie along the x-axis at 0 cm, 1.8 cm,
and 5.3 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 ¡Á 109 N ¡¤ m2/C2.
Answer in units of N
To find the force exerted on q1 by the other two charges, we can use Coulomb's Law, which 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.
Let's calculate the force exerted individually by the two charges and then add them to find the total force.
The formula for Coulomb's Law 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
r is the distance between the charges.
First, let's calculate the force exerted by the +6.5 μC charge (q2) on the +1.4 μC charge (q1):
|q1| = 1.4 μC = 1.4 × 10^-6 C
|q2| = 6.5 μC = 6.5 × 10^-6 C
r = 1.8 cm = 0.018 m
F1 = (8.99 × 10^9 N · m^2/C^2) * (|q1| * |q2|) / r^2
F1 = (8.99 × 10^9 N · m^2/C^2) * (1.4 × 10^-6 C * 6.5 × 10^-6 C) / (0.018 m)^2
Next, let's calculate the force exerted by the -3.9 μC charge (q3) on the +1.4 μC charge (q1):
|q3| = -3.9 μC = -3.9 × 10^-6 C
r = 5.3 cm = 0.053 m
F2 = (8.99 × 10^9 N · m^2/C^2) * (|q1| * |q3|) / r^2
F2 = (8.99 × 10^9 N · m^2/C^2) * (1.4 × 10^-6 C * -3.9 × 10^-6 C) / (0.053 m)^2
Finally, we can find the total force exerted on q1 by adding the forces F1 and F2:
F_total = F1 + F2
Calculate the values using the equations above to find the force exerted on q1 by the other two charges. The answer will be in units of N (Newton).
To calculate the force exerted on q1 by the other two charges, we can use the formula for Coulomb's law:
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 magnitudes of the charges
r is the distance between the charges
Let's calculate the force separately for each combination of charges and then add them up.
1. Force between q1 and q2:
|q1| = 6.5 µC = 6.5 × 10^-6 C
|q2| = 1.4 µC = 1.4 × 10^-6 C
r = 1.8 cm = 0.018 m
F12 = (8.99 × 10^9 N · m^2/C^2) * (|6.5 × 10^-6 C| * |1.4 × 10^-6 C|) / (0.018 m)^2
2. Force between q1 and q3:
|q1| = 6.5 µC = 6.5 × 10^-6 C
|q3| = 3.9 µC = -3.9 × 10^-6 C (negative because it is to the left)
r = 5.3 cm = 0.053 m
F13 = (8.99 × 10^9 N · m^2/C^2) * (|6.5 × 10^-6 C| * |-3.9 × 10^-6 C|) / (0.053 m)^2
3. Calculate the total force by adding up the individual forces:
F_total = F12 + F13
Now we can calculate the force.