A positive charge with Q1= +210-6 C and a negative charge Q2 = -1×10-6 C are located at an equal distance 0.1m from the origin (see below). A third charge Q3=+110-6C is located at the origin.
Calculate the magnitude of the net force exerted on charge Q3
Calculate the direction of the net force exerted on charge Q3.
To calculate the magnitude and direction of the net force exerted on charge Q3, we can use Coulomb's Law and vector addition.
Coulomb's Law states that the electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them:
F = (k * |Q1 * Q3|) / r^2
Where F is the force between the charges, k is Coulomb's constant (approximately 9 × 10^9 N*m^2/C^2), |Q1 * Q3| is the absolute value of the product of the charges, and r is the distance between the charges.
Now, let's calculate the force between Q1 and Q3:
F1 = (k * |Q1 * Q3|) / r^2
= (9 * 10^9 * |2 * 10^-6 * 1 * 10^-6|) / (0.1)^2
Simplifying further,
F1 = 18 * 10^3 N
Similarly, let's calculate the force between Q2 and Q3:
F2 = (k * |Q2 * Q3|) / r^2
= (9 * 10^9 * |-1 * 10^-6 * 1 * 10^-6|) / (0.1)^2
Simplifying further,
F2 = -9 * 10^3 N
Since force is a vector quantity, we need to consider both magnitude and direction. Since Q1 and Q2 have opposite charges, the forces they exert on Q3 will have opposite directions.
The net force on Q3 can be found by summing the individual forces:
F_net = F1 + F2
= 18 * 10^3 N + (-9 * 10^3 N)
= 9 * 10^3 N
So, the magnitude of the net force acting on Q3 is 9 * 10^3 N.
To determine the direction of the net force, we need to consider the signs of the individual forces. Since F1 is positive and F2 is negative, the net force will act in the direction of the positive force. Therefore, the net force on Q3 will be in the same direction as F1.
Hence, the direction of the net force exerted on charge Q3 is in the direction of the positive force, which is away from Q1.