We have a charge q = -0.6 x 10^-6 C at origin. And a vector r = (4 m, 3 m, 0 m). Find the electric field E(r) as a vector expressed in terms of i j and k.
What is the distance in this case? Magnitude of r? Also, how do I find the Electric field as a vector? I'm stuck..
distance=sqrt(16+9+0)=5
E=kq rvector/r^3=kq (4/64,3/27,0)
To find the electric field E(r) as a vector, you can use Coulomb's law. Coulomb's law states that the electric field E created by a point charge q at a distance r from the charge is given by:
E(r) = k * (q / r^2) * r_hat
Where:
- E(r) is the electric field at point r,
- k is Coulomb's constant, approximately equal to 9 x 10^9 N·m^2/C^2,
- q is the charge creating the electric field,
- r is the distance from the charge to the point where you want to find the electric field,
- r_hat is the unit vector in the direction of r.
In this case, you are given the charge q = -0.6 x 10^-6 C and the vector r = (4 m, 3 m, 0 m). To find the electric field E(r), we need to calculate the magnitude of r and the unit vector r_hat.
The distance or magnitude of r can be calculated using the formula:
|r| = √(x^2 + y^2 + z^2)
In this case, |r| = √(4^2 + 3^2 + 0^2) = √(16 + 9 + 0) = √25 = 5 m.
Now, to find the unit vector r_hat, divide each component of r by its magnitude:
r_hat = (4 m / 5 m, 3 m / 5 m, 0 m / 5 m) = (0.8, 0.6, 0)
Finally, substitute the values of k, q, and r_hat into the equation for E(r):
E(r) = k * (q / r^2) * r_hat
E(r) = (9 x 10^9 N·m^2/C^2) * (-0.6 x 10^-6 C / (5 m)^2) * (0.8 i + 0.6 j + 0 k)
Thus, the electric field E(r) as a vector expressed in terms of i, j, and k would be:
E(r) = (-2.88 x 10^2 i - 2.16 x 10^2 j) N/C