Three charges lie along the x axis the positive charge Q1 = 4mC is at X=2m and the postion of postive Q2 = 8uC is at the origin Q3 is placed on the x axis what is the sign on Q3 and why
To determine the sign of Q3, we need to analyze the electric field created by Q1 and Q2 at different positions along the x-axis.
First, let's calculate the electric field created by Q1 at a point on the x-axis where Q3 is located. The formula to calculate the electric field due to a point charge is:
E1 = k * (Q1 / r1^2),
where E1 is the electric field at the point on the x-axis, k is Coulomb's constant (8.99 * 10^9 Nm^2/C^2), Q1 is the charge of Q1 (4 mC, or 4 * 10^-3 C), and r1 is the distance from Q1 to the point on the x-axis.
Since Q1 is located at X=2m, the distance r1 from Q1 to the point on the x-axis can be calculated as:
r1 = X - 2,
where X is the coordinate of the point on the x-axis where Q3 is located. Let's assume X is positive.
Similarly, let's calculate the electric field created by Q2 at the same point on the x-axis. The formula is:
E2 = k * (Q2 / r2^2),
where E2 is the electric field at the point on the x-axis, Q2 is the charge of Q2 (8 uC, or 8 * 10^-6 C), and r2 is the distance from Q2 to the point on the x-axis.
Since Q2 is at the origin, the distance r2 from Q2 to the point on the x-axis is simply equal to X, the coordinate of the point on the x-axis where Q3 is located.
Now, we can determine the sign of Q3 based on the direction of the net electric field. If the net electric field points towards Q3, it means Q3 is negative, and if the net electric field points away from Q3, it means Q3 is positive.
To find the net electric field, we need to consider the vector sum of the electric fields due to Q1 and Q2. Since the electric fields are vectors, we can use the principle of superposition to find the resultant electric field.
Net Electric Field (E_net) = E1 + E2
Now, let's analyze the different cases:
1. If E_net > 0:
- This means the net electric field is pointing away from the point on the x-axis.
- Therefore, the charge on Q3 must be positive to create a net electric field pointing away from Q3.
- In this case, Q3 is positive.
2. If E_net < 0:
- This means the net electric field is pointing towards the point on the x-axis.
- Therefore, the charge on Q3 must be negative to create a net electric field pointing towards Q3.
- In this case, Q3 is negative.
3. If E_net = 0:
- This means the net electric field is zero at the point on the x-axis.
- Therefore, the charge on Q3 must also be zero or neutral.
- In this case, Q3 has no charge.
To determine the exact sign of Q3, we need to calculate the values of E_net at different positions on the x-axis, and see if it is positive, negative, or zero.