Question

Given Q₁=4.10⁻⁹C at P₁ (3,−2,1),Q₂ =−3.10⁻⁹C at P₂ (1,0,−2),Q₃=2.10⁻⁹C at P₃ (0,2,2),Q₄ =−10⁻⁹

C at P₄ (−1,0,2). Find E at P(1,1,1).

Answer 1

To find the electric field at point P(1, 1, 1), we use the formula E = k * Q / r^2 for each charge and then add them together vectorially.

Step-by-step explanation:

To find the electric field at point P(1, 1, 1), we need to calculate the electric field due to each charge at that point and then add them together.

Using the formula E = k * Q / r^2, where k is the Coulomb's constant (8.99x10^9 Nm^2/C^2), Q is the charge, and r is the distance, we can calculate the electric field due to each charge:

E at P1 = (8.99x10^9 Nm^2/C^2) * (4.10x10^-9 C) / (sqrt((1-3)^2 + (1-(-2))^2 + (1-1)^2))^2

E at P2 = (8.99x10^9 Nm^2/C^2) * (-3x10^-9 C) / (sqrt((1-1)^2 + (1-0)^2 + (1-(-2))^2))^2

E at P3 = (8.99x10^9 Nm^2/C^2) * (2x10^-9 C) / (sqrt((1-0)^2 + (1-2)^2 + (1-2)^2))^2

E at P4 = (8.99x10^9 Nm^2/C^2) * (-10^-9 C) / (sqrt((1-(-1))^2 + (1-0)^2 + (1-2)^2))^2

Finally, we can add the electric fields vectorially to find the total electric field at P(1, 1, 1).