Two positive charges, each of magnitude q, are on the y-axis at points y = + a and y = -a. Where would a third positive charge of the same magnitude be located for the net force on the third charge to be zero?
a) at the origin
b) at y = 2a
c) at y = -2a
d) at y = -a
I said A is this right?
Yup its correct.
Well, let's think about this creatively. If two positive charges of the same magnitude are located symmetrically on the y-axis, and we want the net force on a third positive charge to be zero, where should it be located?
Hmm, it seems like a setup for a quick physics joke!
Why did the positive charge go to a comedy club?
Because it wanted to find its equilibrium point and be "neutral" on stage!
So, the correct answer is indeed "a) at the origin." Well done!
To find the location where the net force on the third positive charge is zero, we need to consider the forces exerted by the other two charges on it.
Let's label the two positive charges as q1 and q2. q1 is located at y = +a, and q2 is located at y = -a.
The force between two charges is given by Coulomb's Law:
F = k * |q1 * q2| / r^2
where F is the force, k is the electrostatic constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Since the magnitudes of all three charges are the same, we can ignore the constants in Coulomb's Law and focus on the relative distances to determine the direction of the forces.
The distance between the third charge (q3) and the other two charges can be considered as r1 and r2.
From the given information, we know that q1 and q2 are equidistant from q3. Therefore, the magnitudes of the forces between q3 and q1 (F1) and between q3 and q2 (F2) are the same.
Since forces are vectors, when two forces have the same magnitude but are in opposite directions, their vector sum (net force) is zero. The forces F1 and F2 on q3 are in opposite directions since q1 and q2 have opposite signs.
Given this, the net force on q3 is zero when it is located at the midpoint between q1 and q2, which is at the origin.
Therefore, the correct answer is a) at the origin.
To find the location where the net force on the third positive charge is zero, we can apply the principle of superposition of forces.
The force between two charges can be determined using Coulomb's Law: F = k * (q1 * q2) / r^2, where F is the force between the charges, k is the electrostatic constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them.
Let's denote the third positive charge as Q, the charge at y = +a as q1, and the charge at y = -a as q2.
The net force on charge Q is the vector sum of the forces it experiences due to q1 and q2. Since both q1 and q2 are positive charges, they repel each other, and thus their forces on charge Q have the same direction.
If we consider the forces on charge Q due to q1 (located at y = +a) and q2 (located at y = -a) individually, we can analyze their directions and magnitudes:
1. Force due to q1: The force exerted by q1 on Q is directed away from q1 along the y-axis, i.e., in the negative y-direction. The magnitude of this force is given by F1 = k * ((q * q) / (a^2)).
2. Force due to q2: The force exerted by q2 on Q is directed away from q2 along the y-axis, i.e., in the positive y-direction. The magnitude of this force is also given by F2 = k * ((q * q) / (a^2)).
Since the magnitudes of the forces F1 and F2 are the same, and they have opposite directions, these forces cancel each other out when their vectors are added.
Considering the forces due to q1 and q2:
- The force due to q1 is directed downward (negative y-direction).
- The force due to q2 is directed upward (positive y-direction).
When these forces cancel out, the net force on charge Q will be zero. This will occur when the magnitudes of F1 and F2 are equal.
In this scenario, the only possible location for charge Q to experience a net force of zero is at the origin, i.e., at point (0, 0). Therefore, your answer of option A is correct.