Find the magnitude and direction of the net electrostatic force exerted on the point charge q3 in the figure below, where q = +2.5 μC and d = 28 cm. The picture is of a square. q1=+q, q2=-2q, q3=-3q, q4=-4
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To find the magnitude and direction of the net electrostatic force exerted on the point charge q3, we need to consider the individual forces acting on it due to each of the other charges (q1, q2, and q4).
1. Calculate the force between q3 and q1:
The force between two charges is given by Coulomb's Law:
F1 = k * |q3| * |q1| / r1^2
where k is the electrostatic constant (k ≈ 9 × 10^9 Nm^2/C^2), |q3| is the magnitude of charge q3, |q1| is the magnitude of charge q1, and r1 is the distance between q3 and q1.
Since q = +2.5 μC and q1 = +q, we have |q3| = 3q, |q1| = q, and r1 = d. Substituting these values:
F1 = k * |q3| * |q1| / r1^2
= (9 × 10^9 Nm^2/C^2) * (3q) * (q) / (0.28 m)^2
2. Calculate the force between q3 and q2:
Following the same procedure as above, we find:
F2 = k * |q3| * |q2| / r2^2
= (9 × 10^9 Nm^2/C^2) * (3q) * (2q) / (0.28 m)^2
3. Calculate the force between q3 and q4:
Again, using Coulomb's Law:
F3 = k * |q3| * |q4| / r3^2
= (9 × 10^9 Nm^2/C^2) * (3q) * (4q) / (0.28 m)^2
4. Calculate the net force on q3:
The net force (F_net) is the vector sum of the individual forces. To find the magnitude and direction of F_net, we can use the Pythagorean theorem:
F_net = sqrt(F1^2 + F2^2 + F3^2)
5. Determine the direction:
The direction of the net force can be determined by finding the angle (θ) between the net force vector and the positive x-axis, using trigonometry:
θ = atan(F2/F1)
Calculating these values and plugging in the given numbers, we can then find the magnitude and direction of the net electrostatic force exerted on q3 in the figure.
To find the magnitude and direction of the net electrostatic force exerted on the point charge q3, we need to consider the individual electrostatic forces between q3 and each of the other charges q1, q2, and q4.
First, we need to determine the value of q3 in terms of q. Given that q3 = -3q, we can substitute the appropriate value for q in our calculations.
Next, we can calculate the magnitude of the electrostatic forces between q3 and each of the other charges using Coulomb's Law:
The electrostatic force between two point charges q1 and q3 is given by:
F1 = k * |q1| * |q3| / r^2, where k is the electrostatic constant, |q1| and |q3| are the absolute values of the charges, and r is the distance between them.
Similarly, the force between q2 and q3 is:
F2 = k * |q2| * |q3| / r^2
And the force between q4 and q3:
F3 = k * |q4| * |q3| / r^2
To calculate the net electrostatic force on q3, we need to add up the individual forces vectorially. Since we are dealing with a square configuration of charges, we can assume that the forces along two opposite sides will cancel each other out, leaving only diagonal forces contributing to the net force on q3.
Finally, to find the direction of the net electrostatic force, we need to determine the angle between the resultant force vector and one of the sides of the square.
By performing these calculations, we can find both the magnitude and direction of the net electrostatic force exerted on q3.