Two point charges are placed on the x axis as follows: Charge q1= 4.20 is located at x= 0.185 , and charge q2= 4.80 is at x= -0.280 . What are the magnitude and direction of the net force exerted by these two charges on a negative point charge A = -0.625placed at the origin?
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To find the magnitude and direction of the net force exerted by the charges on point charge A, we can use Coulomb's Law.
Step 1: Calculate the force exerted on point charge A by q1.
Given:
Charge q1 = 4.20
Position of q1, x1 = 0.185
Position of charge A, xA = 0 (located at the origin)
The distance between q1 and charge A, r1A = x1 - xA = 0.185 - 0 = 0.185
Using Coulomb's Law:
Force exerted by q1 on charge A, F1A = (k * |q1| * |A|) / r1A^2
where k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2)
Plugging in the values:
F1A = (8.99 x 10^9 Nm^2/C^2 * 4.20 C * 0.625 C) / (0.185 m)^2
Step 2: Calculate the force exerted on point charge A by q2.
Given:
Charge q2 = 4.80
Position of q2, x2 = -0.280
Position of charge A, xA = 0 (located at the origin)
The distance between q2 and charge A, r2A = x2 - xA = -0.280 - 0 = -0.280
Using Coulomb's Law:
Force exerted by q2 on charge A, F2A = (k * |q2| * |A|) / r2A^2
Plugging in the values:
F2A = (8.99 x 10^9 Nm^2/C^2 * 4.80 C * 0.625 C) / (-0.280 m)^2
Step 3: Calculate the net force
The net force, Fnet, is the sum of the individual forces:
Fnet = F1A + F2A
Step 4: Determine the magnitude and direction
The magnitude of the net force is given by |Fnet| = sqrt(Fnetx^2 + Fnety^2), where Fnetx and Fnety are the x and y components of the net force.
The direction of the net force can be determined by finding the angle it makes with the positive x-axis, using the equation tan(theta) = Fnety / Fnetx.
Now, calculate the values of F1A, F2A, Fnet, |Fnet|, and the direction theta.
To find the magnitude and direction of the net force exerted by the two charges on point charge A, 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 the force between two charges is given by:
F = (k * |q1| * |q2|) / r^2
where F is the magnitude of the force, k is the electrostatic constant with a value of approximately 9 × 10^9 N m^2/C^2, |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.
In this case, the distance between charge q1 and point charge A is the x-coordinate of q1 (0.185), and the distance between charge q2 and point charge A is the absolute value of the x-coordinate of q2 (-0.280).
First, let's calculate the force exerted by q1 on A:
F1 = (k * |q1| * |A|) / r1^2
F1 = (9 * 10^9 N m^2/C^2) * (4.20 C) * (0.625 C) / (0.185 m)^2
F1 ≈ 2.713 N
The direction of this force would be the same as the direction from q1 to A.
Next, let's calculate the force exerted by q2 on A:
F2 = (k * |q2| * |A|) / r2^2
F2 = (9 * 10^9 N m^2/C^2) * (4.80 C) * (0.625 C) / (0.280 m)^2
F2 ≈ 2.864 N
The direction of this force would be the same as the direction from q2 to A.
To find the net force, we need to find the vector sum of F1 and F2. Since they are in the same direction, we can simply add their magnitudes:
Fnet = F1 + F2
Fnet ≈ 2.713 N + 2.864 N
Fnet ≈ 5.577 N
The direction of the net force would be the same as the direction from q1 to A or from q2 to A.
Therefore, the magnitude of the net force exerted by these two charges on the negative point charge A is approximately 5.577 N in the direction from q1 to A or from q2 to A.