Final answer:
The total force exerted by the two charges on the third charge is approximately 0.090 N and is directed towards q2.
Step-by-step explanation:
To find the total force exerted by the two charges on the third charge, we can use Coulomb's law. Coulomb's law 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. The formula for Coulomb's law is:
F = k * (|q1 * q2| / r^2)
Where F is the force, k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
For the given problem, the charges and distances are:
- q1 = -1.50 nC
- q2 = +3.20 nC
- q3 = +5.00 nC
- Distance between q1 and q3 = 0.60 m
- Distance between q2 and q3 = 0.40 m
Using Coulomb's law, we can calculate the force exerted by each charge on q3:
- Force exerted by q1 on q3: F1 = k * (|q1 * q3| / r1^2)
- Force exerted by q2 on q3: F2 = k * (|q2 * q3| / r2^2)
Substituting the given values, we get:
- F1 = 8.99 x 10^9 * (|-1.50 nC * 5.00 nC| / (0.60 m)^2)
- F2 = 8.99 x 10^9 * (|3.20 nC * 5.00 nC| / (0.40 m)^2)
Calculating the values, we get:
- F1 ≈ -0.015 N (negative sign indicates the direction towards q1)
- F2 ≈ 0.090 N (positive sign indicates the direction towards q2)
To find the total force, we need to calculate the vector sum of these two forces:
- Total force = √((F1^2) + (F2^2)) ≈ √((0.015 N)^2 + (0.090 N)^2) ≈ 0.090 N
Therefore, the total force exerted by the two charges on q3 is approximately 0.090 N, and it is directed towards q2.