Three positive point charges are arranged in
a triangular pattern in a plane as shown.
+
2 nC
+
4 nC
+
6 nC
Distance between all: 7 m
I don't know how to d this part:
Find the magnitude of the net electric force
on the 4 nC charge. The Coulomb constant is
8.98755 × 109 N · m2
/C
2
.
Answer in units of N.
017 (part 2 of 2) 10.0 points
What is the direction of this force (measured
from the positive x-axis as an angle between
−180◦and 180◦
, with counterclockwise positive)?
Answer in units of ◦
To find the magnitude of the net electric force on the 4 nC charge, we can use the principle of superposition. The net force is the vector sum of the individual forces between the charges.
The electric force between two charges is given by Coulomb's law:
F = k * (q1 * q2) / r^2
Where F is the force between the charges, k is the Coulomb constant (8.98755 × 10^9 N · m^2/C^2), q1 and q2 are the charges, and r is the distance between them.
In this case, we have three point charges (+2 nC, +4 nC, and +6 nC) arranged in a triangular pattern. The distances between all three charges are 7 m.
To find the net force on the 4 nC charge, we calculate the force between the 4 nC charge and the +2 nC charge, the force between the 4 nC charge and the +4 nC charge, and the force between the 4 nC charge and the +6 nC charge.
Once we have calculated these forces, we can sum them up as vectors to find the net force.
Let's calculate the individual forces first:
Force between the 4 nC charge and the +2 nC charge:
F1 = k * (4 nC * 2 nC) / (7 m)^2
Force between the 4 nC charge and the +4 nC charge:
F2 = k * (4 nC * 4 nC) / (7 m)^2
Force between the 4 nC charge and the +6 nC charge:
F3 = k * (4 nC * 6 nC) / (7 m)^2
Now, let's calculate the net force:
Net Force = F1 + F2 + F3
Finally, to find the direction of this force measured from the positive x-axis as an angle between -180° and 180°, we can use trigonometry. We can find the angle using the following formula:
Angle = atan2(Fy, Fx)
Where Fx is the horizontal component of the net force and Fy is the vertical component of the net force.
Now that we have the magnitude and direction of the net electric force, we have answered both parts of the question.