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
To find the force exerted on q1 by the other two charges, we can use the principle of superposition. According to this principle, the total force on a charge due to multiple charges is the vector sum of the individual forces.
The force between two charges can be calculated using Coulomb's Law, which states that the force (F) between two point charges (q1 and q2) is given by the equation:
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
In this case, we have three charges (+6.0 µC, +1.7 µC, and -2.3 µC) lying along the x-axis at 0 cm, 1.7 cm, and 6.0 cm, respectively.
To find the force exerted by the other two charges (q2 and q3) on q1, we need to calculate the force between each pair of charges (q1-q2 and q1-q3) using Coulomb's Law and then add them together.
Let's calculate the force exerted by the charges q2 and q3 on q1:
Force exerted by q2 on q1:
- q1 = +6.0 µC
- q2 = +1.7 µC
- r2 = 1.7 cm = 0.017 m (converted from centimeters to meters)
- Using Coulomb's Law:
F2 = (k * |q1 * q2|) / r2^2
Force exerted by q3 on q1:
- q1 = +6.0 µC
- q3 = -2.3 µC
- r3 = 6.0 cm = 0.06 m (converted from centimeters to meters)
- Using Coulomb's Law:
F3 = (k * |q1 * q3|) / r3^2
Finally, we can add the forces F2 and F3 to find the total force exerted on q1 by the other two charges:
Total Force = F2 + F3
Now you can substitute the values into the equations and calculate the individual forces as well as the total force.