To calculate the electric force on a 10 nC charge located at (0,2,4) due to the point charges at (3,2,1) and (-1,-2,-3), we can use Coulomb's law. Coulomb's law states that the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Step 1: Calculate the distance between the charge at (0,2,4) and the charge at (3,2,1).
The distance between two points in three-dimensional space can be calculated using the distance formula:
d = √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
Substituting the values, we get:
d = √((3-0)^2 + (2-2)^2 + (1-4)^2)
d = √(9 + 0 + 9)
d = √18
d = 3√2
Step 2: Calculate the electric force between the charges.
Using Coulomb's law, the electric force (F) between two point charges (q1 and q2) is given by the formula:
F = (k * |q1 * q2|) / d^2
where k is the electrostatic constant.
Substituting the values, we get:
F = (k * |10 * 2 * 10^-9 * 4 * 10^-9|) / (3√2)^2
F = (9 * 10^9 * 20 * 10^-18) / (3√2)^2
F = (180 * 10^-9) / (9 * 2)
F = 10 * 10^-9
F = 10 * 10^-9 N
Therefore, the electric force on the 10 nC charge located at (0,2,4) due to the point charges at (3,2,1) and (-1,-2,-3) is 10 * 10^-9 Newtons.
To calculate the electric field intensity at the point (0,2,4), we can use the formula:
E = F / q
where E is the electric field intensity and q is the charge experiencing the force.
Substituting the values, we get:
E = (10 * 10^-9 N) / (10 * 10^-9 C)
E = 1 N/C
Therefore, the electric field intensity at the point (0,2,4) is 1 N/C.