A particle with charge -5.0 μC is placed at -2.0 m, and a particle with charge 5.0 μC is placed at +2.0m. What is the electric field at the origin?
To find the electric field at the origin due to the two charged particles, we can use the principle of superposition. The electric field at a point is the vector sum of the electric fields produced by each individual charge.
Let's calculate the electric field due to each charge separately:
1. Electric field due to the -5.0 μC charge:
The electric field produced by a point charge is given by Coulomb's law:
E1 = k * (q1 / r1^2), where k is the electrostatic constant, q1 is the charge, and r1 is the distance between the charge and the point at which we want to calculate the electric field.
Plugging in the values:
E1 = k * ((-5.0 × 10^(-6)) C) / (-2.0 m)^2
2. Electric field due to the +5.0 μC charge:
Similarly, using Coulomb's law:
E2 = k * (q2 / r2^2), where q2 is the charge and r2 is the distance between the other charge and the point at which we want to calculate the electric field.
Plugging in the values:
E2 = k * ((5.0 × 10^(-6)) C) / (2.0 m)^2
Now, we can calculate the total electric field at the origin by adding the electric fields due to each charge:
E_total = E1 + E2
Note that the direction of the electric field due to the -5.0 μC charge will be towards the left (negative x-direction), while the direction of the electric field due to the +5.0 μC charge will be towards the right (positive x-direction). Thus, we need to take into account the direction of the electric fields while adding them.
Once we have both the magnitudes and directions of the electric fields, we can determine the net electric field at the origin.