a point charge q=-8.0nC is located at origin . find electric field vector at point x=1.2m,y=-1.6m

To find the electric field vector at the given point due to the point charge at the origin, we can use Coulomb's law.

The electric field vector at a point is given by the equation:

E = (k * q) / r^2

where:
- E is the electric field vector,
- k is the electrostatic constant (k = 8.99 x 10^9 N m^2 / C^2),
- q is the charge of the point charge (in this case, q = -8.0 nC = -8.0 x 10^-9 C),
- r is the distance between the charge and the point of interest.

In this case, the point of interest is at coordinates (x = 1.2 m, y = -1.6 m).

We can start by calculating the distance between the charge and the point of interest:

r = sqrt(x^2 + y^2)
= sqrt((1.2 m)^2 + (-1.6 m)^2)
= sqrt(1.44 m^2 + 2.56 m^2)
= sqrt(3.2 m^2)
= 1.79 m

Now, we can substitute the values into the equation for the electric field vector:

E = (k * q) / r^2
= (8.99 x 10^9 N m^2 / C^2) * (-8.0 x 10^-9 C) / (1.79 m)^2

Calculating this expression will give us the electric field vector at the given point.

To find the electric field vector at a point, we can use the formula for the electric field due to a point charge:

E = k * (q / r^2) * r_hat

Where:
E: Electric field vector
k: Coulomb's constant (k = 9 x 10^9 Nm^2/C^2)
q: Charge of the point charge
r: Distance from the point charge to the point where we want to find the electric field
r_hat: Unit vector pointing from the point charge towards the point where we want to find the electric field

In this case, we have:
q = -8.0 nC = -8.0 x 10^-9 C (Given charge)
r = √((1.2)^2 + (-1.6)^2) = √(1.44 + 2.56) = √4 = 2.0 m (Distance from the origin to the given point)
r_hat = (1.2/2.0)i + (-1.6/2.0)j = 0.6i - 0.8j (Unit vector pointing from the origin to the given point)

Now, substitute these values into the formula to find the electric field vector:

E = (9 x 10^9 Nm^2/C^2) * (-8.0 x 10^-9 C) / (2.0 m)^2 * (0.6i - 0.8j)

E = (9 x 10^9) * (-8.0 x 10^-9) / 4.0 * (0.6i - 0.8j)

E = -108i + 144j N/C

Therefore, the electric field vector at the point (x = 1.2 m, y = -1.6 m) is -108i + 144j N/C.

We are not interested in the name of your school.

The electric field due to a point charge is explained at
http://en.wikipedia.org/wiki/Coulomb's_law