Final answer:
To determine the electric field at point P due to a charge q, calculate the distance between q and P, then use this distance and Coulomb's law to find the electric field's magnitude and direction.
Step-by-step explanation:
To find the electric field at point P (0m, -4m, 3m) due to a charge q (equal to 1 µC) at point (1m, 2m, 4m), we use Coulomb's law. The electric field E due to a point charge q at a distance r is given by E = k * |q| / r^2, where k is Coulomb's constant (approximately 8.988 × 10^9 Nm^2/C^2). First, we need to calculate the distance r between the charge and point P, which is the magnitude of the vector from q to P.
The vector from q to P is (0 - 1, -4 - 2, 3 -4) = (-1, -6, -1) meters. The magnitude of this vector is r = √((-1)^2 + (-6)^2 + (-1)^2) meters.
Next, we find the unit vector u_r which points from q to P by dividing each component of the vector from q to P by its magnitude. This unit vector is needed to determine the direction of the electric field.
Finally, we calculate the electric field E by multiplying the unit vector u_r by the scalar value of the electric field magnitude, which is k * |q| / r^2.