Final answer:
The net electric field at point P1, in cartesian unit-vector notation, can be calculated by adding the electric fields from the two charge elements using Coulomb's law and the principle of superposition.
Step-by-step explanation:
The net electric field at point P1, denoted as E(P1), is the vector sum of the electric fields from each charge element. We can represent this as E(P1) = E1 + E2, where E1 and E2 are the electric fields from the two charge elements.
Using cartesian unit-vector notation, we can write the expression as E(P1) = E1i + E2j + E3k, where i, j, and k are the unit vectors in the x, y, and z directions respectively. The electric fields E1 and E2 can be calculated using Coulomb's law and the principle of superposition.
For example, if E1 = k*q1/r1^2 * (-cosθ1 i + sinθ1 j) and E2 = k*q2/r2^2 * (cosθ2 i + sinθ2 j), the net electric field E(P1) would be E(P1) = (k*q1/r1^2 * (-cosθ1) + k*q2/r2^2 * (cosθ2))i + (k*q1/r1^2 * sinθ1 + k*q2/r2^2 * sinθ2)j + E3k, where k is the Coulomb's constant and q1, q2, r1, r2, θ1, θ2 represent the charges, distances, and angles involved.