To calculate the magnitude of the electric field at a point located 15 cm directly north of a point charge, we can use Coulomb’s Law.
Coulomb’s Law states that the magnitude of the electric field (E) created by a point charge (Q) at a distance (r) from the charge is given by the equation:
E = k * (Q / r²)
Where: - E is the magnitude of the electric field - k is the electrostatic constant, equal to 9 × 10⁹ m²N/C² - Q is the charge of the point charge - r is the distance from the point charge
In this case, the charge of the point charge is Q = -15.0 × 10-⁶ C, and the distance from the point charge is r = 15 cm = 0.15 m.
Plugging these values into the equation, we get:
E = (9 × 10⁹ m²N/C²) * (-15.0 × 10-⁶ C) / (0.15 m)²
Simplifying the equation, we have:
E = (9 × 10⁹ m²N/C²) * (-15.0 × 10-⁶ C) / (0.15 m)² = -135 × 10³ N/C / 0.0225 m² = -135 × 10³ N/C * (1 / 0.0225) m² = -135 × 10³ N/C * 44.44 m² = -6 × 10⁶ N/C
Therefore, the magnitude of the electric field at a point located 15 cm directly north of the point charge is 6 × 10⁶ N/C. The negative sign indicates that the electric field is directed towards the point charge, which is expected since the charge is negative.