Electric Field
1. **Problem Statement:** We want to find the electric field $E$ at a distance of 3 meters from a point charge of $+2\,\mu C$ (microcoulombs).
2. **Definition:** The electric field $E$ is the force experienced per unit charge at a point in space due to another charge.
3. **Formula:** The electric field due to a point charge is given by
$$E = \frac{kq}{r^2}$$
where:
- $k = 9 \times 10^9$ N m$^2$/C$^2$ (Coulomb's constant),
- $q$ is the charge,
- $r$ is the distance from the charge.
4. **Given values:**
- $q = +2\,\mu C = 2 \times 10^{-6}$ C,
- $r = 3$ m.
5. **Calculation:** Substitute the values into the formula:
$$E = \frac{9 \times 10^9 \times 2 \times 10^{-6}}{3^2} = \frac{9 \times 10^9 \times 2 \times 10^{-6}}{9}$$
6. Simplify the denominator:
$$E = \frac{18 \times 10^3}{9} = 2 \times 10^3 = 2000$$
7. **Result:** The electric field at 3 meters from the charge is $2000$ N/C.
8. **Direction:** Since the charge is positive, the electric field points away from the charge.
This means if you place a small positive test charge at 3 meters, it will feel a force pushing it directly away from the $+2\,\mu C$ charge.