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
jopN
To calculate 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 given by:
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 between q1 and q2:
F1 = k * (|q1| * |q2| / r^2)
F1 = (8.99 × 10^9 N · m^2 / C^2) * (6.0 µC * 1.7 µC / (0.017 m)^2)
F1 = (8.99 × 10^9 N · m^2 / C^2) * (6.0 × 10^-6 C * 1.7 × 10^-6 C / 0.000289 m^2)
F1 = (8.99 × 10^9 N · m^2 / C^2) * (1.02 × 10^-11 C^2 / 0.000289 m^2)
F1 = (8.99 × 10^9 N · m^2) * (1.02 × 10^-11 C^2 / 0.000289 m^2)
F1 ≈ 2.96 * 10^-3 N
Now let's calculate the force between q1 and q3:
F2 = k * (|q1| * |q3| / r^2)
F2 = (8.99 × 10^9 N · m^2 / C^2) * (6.0 µC * 2.3 µC / (0.06 m)^2)
F2 = (8.99 × 10^9 N · m^2 / C^2) * (6.0 × 10^-6 C * 2.3 × 10^-6 C / 0.0036 m^2)
F2 = (8.99 × 10^9 N · m^2 / C^2) * (1.38 × 10^-11 C^2 / 0.0036 m^2)
F2 = (8.99 × 10^9 N · m^2) * (1.38 × 10^-11 C^2 / 0.0036 m^2)
F2 ≈ 3.46 * 10^-3 N
Finally, we can calculate the total force on q1:
Total force = F1 + F2
Total force ≈ 2.96 * 10^-3 N + 3.46 * 10^-3 N
Total force ≈ 6.42 * 10^-3 N
Therefore, the force exerted on q1 by the other two charges is approximately 6.42 * 10^-3 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 charged objects is proportional to the product of their charges and inversely proportional to the square of the distance between them.
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 * q2| is the product of the magnitudes of the charges, and
r^2 is the square of the distance between the charges.
In this case, we have three charges: q1 = +6.0 µC, q2 = +1.7 µC, and q3 = -2.3 µC, and they are located at distances of 0 cm, 1.7 cm, and 6.0 cm from q1 along the x-axis, respectively.
First, let's calculate the force exerted on q1 by q2:
F12 = (k * |q1 * q2|) / r12^2
Substituting the values:
F12 = (8.99 × 10^9 N · m^2/C^2 * |+6.0 µC * +1.7 µC|) / (1.7 cm)^2
The absolute value of the product of the charges is simply the product:
|q1 * q2| = +6.0 µC * +1.7 µC = +10.2 µC^2
Converting the charge to Coulombs:
|q1 * q2| = 10.2 * 10^-6 C^2
Now, let's substitute all the values into the equation:
F12 = (8.99 × 10^9 N · m^2/C^2 * 10.2 * 10^-6 C^2) / (1.7 cm)^2
Simplifying the equation:
F12 = (8.99 × 10^9 N · m^2 * 10.2 * 10^-6) / (1.7^2 * 10^-4) C^2
Canceling out the units:
F12 = 9.174 N
So, the force exerted on q1 by q2 is 9.174 N to the right.
Next, let's calculate the force exerted on q1 by q3:
F13 = (k * |q1 * q3|) / r13^2
Substituting the values:
F13 = (8.99 × 10^9 N · m^2/C^2 * |+6.0 µC * -2.3 µC|) / (6.0 cm)^2
The absolute value of the product of the charges is simply the product:
|q1 * q3| = +6.0 µC * -2.3 µC = -13.8 µC^2
Converting the charge to Coulombs:
|q1 * q3| = -13.8 * 10^-6 C^2
Now, let's substitute all the values into the equation:
F13 = (8.99 × 10^9 N · m^2/C^2 * -13.8 * 10^-6 C^2) / (6.0 cm)^2
Simplifying the equation:
F13 = (8.99 × 10^9 N · m^2 * -13.8 * 10^-6) / (6.0^2 * 10^-4) C^2
Canceling out the units:
F13 = - 1.655 N
So, the force exerted on q1 by q3 is 1.655 N to the left.
Now, since the forces are along the x-axis, we can simply add the magnitudes of the forces to get the net force:
Net force = |F12| + |F13| = 9.174 N + 1.655 N
Net force = 10.829 N (to the right)
So, the net force exerted on q1 by the other two charges is 10.829 N to the right.