Three point charges are on the x axis: −9 μC at −3 m, 2 μC at the origin, and −5 μC at 3m.
Find the force on the first charge. The value of the Coulomb constant is 8.98755 × 109 N · m2/C2.
Answer in units of N.
well the force from the - charge is opposite direction than the force from the + charge.
force12=(-k(-9)(2)/3^2)
force13=(-l)(-9)(-5)/6^2
notice I did not type 1e-12 in each numerator.
add the forces.
To find the force on the first charge, we can use the formula for the force between two point charges given by Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the two charges,
k is the Coulomb constant (k = 8.98755 × 10^9 N · m^2/C^2),
q1 and q2 are the charges,
and r is the distance between the charges.
In this case, the first charge (q1) is -9 μC, the second charge (q2) is 2 μC, and the distance between the charges (r) is -3 m.
Plugging these values into the formula, we have:
F = (8.98755 × 10^9 N · m^2/C^2) * |-9 μC * 2 μC| / (-3 m)^2
Calculating:
F = (8.98755 × 10^9 N · m^2/C^2) * (|-9 μC * 2 μC| / (-3 m)^2)
= (8.98755 × 10^9 N · m^2/C^2) * (18 μC^2 / 9 m^2)
= (8.98755 × 10^9 N · m^2/C^2) * (2 μC^2 / m^2)
= 17.9751 × 10^9 N · μC^2 / m^2
Converting μC^2 to C^2 (1 μC = 10^-6 C):
F = 17.9751 × 10^9 N · (10^-6 C)^2 / m^2
= 17.9751 × 10^9 N · (10^-12 C^2) / m^2
= 17.9751 × 10^-3 N / m^2
Therefore, the force on the first charge is approximately 0.0179751 N.
To find the force on the first charge, we need to use the formula for electric force:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the force between the two charges.
- k is the Coulomb constant, which is 8.98755 × 10^9 N · m^2/C^2.
- q1 and q2 are the magnitudes of the two charges.
- r is the distance between the charges.
Given:
- |q1| = 9 μC = 9 × 10^-6 C
- |q2| = 2 μC = 2 × 10^-6 C
- |q3| = 5 μC = 5 × 10^-6 C
- r1 = 3 m
- r2 = 0 m (since it's at the origin)
- r3 = 3 m
Now, let's calculate the force between the first charge and the second charge and the force between the first charge and the third charge. Then, we'll add these two forces to find the total force on the first charge.
Force between the first charge and the second charge:
F1-2 = k * (|q1| * |q2|) / r1^2
= (8.98755 × 10^9 N · m^2/C^2) * ((9 × 10^-6 C) * (2 × 10^-6 C)) / (3 m)^2
= (8.98755 × 10^9 N · m^2/C^2) * (1.8 × 10^-11 C^2) / 9 m^2
= 1.79751 × 10^-2 N
Force between the first charge and the third charge:
F1-3 = k * (|q1| * |q3|) / r3^2
= (8.98755 × 10^9 N · m^2/C^2) * ((9 × 10^-6 C) * (5 × 10^-6 C)) / (3 m)^2
= (8.98755 × 10^9 N · m^2/C^2) * (4.5 × 10^-11 C^2) / 9 m^2
= 4.49254 × 10^-2 N
Total force on the first charge:
Ftotal = F1-2 + F1-3
= 1.79751 × 10^-2 N + 4.49254 × 10^-2 N
= 6.29005 × 10^-2 N
Therefore, the force on the first charge is approximately 6.29005 × 10^-2 N.