a point charge q=-8.0nC is located at origin . find electric field vector at point x=1.2m,y=-1.6m
r = sqrt(x^2+y^2) = 2 m
E =k•q/r^2 =9•10^9•8•10^-9/2^2 =18 V/m (directed to the charge)
-18 v/m
To find the electric field at a point due to a point charge, we can use the formula:
E = (k * q) / r^2,
where E is the electric field, k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the point charge and the point where we want to find the electric field.
In this case, the charge q is -8.0 nC (where nC denotes nanocoulombs) and the point where we want to find the electric field is at coordinates (x, y) = (1.2m, -1.6m).
First, we need to calculate the distance (r) between the point charge and the point (1.2m, -1.6m). The distance can be found using the Pythagorean theorem:
r = sqrt(x^2 + y^2),
where x and y are the coordinates of the point.
Substituting the given values into the equation, we have:
r = sqrt((1.2m)^2 + (-1.6m)^2)
= sqrt(1.44m^2 + 2.56m^2)
= sqrt(3.20m^2)
= 1.79m.
Now that we have the distance, we can substitute the values of q and r into the formula for the electric field:
E = (k * q) / r^2
= (8.99 x 10^9 Nm^2/C^2) * (-8.0 x 10^-9 C) / (1.79m)^2.
Calculating this expression will give us the electric field vector at the given point.