Calculate the magnitude and direction of the electric field at a point 20cm from a point charge of magnitude Q= -2×10^-6.
To calculate the magnitude and direction of the electric field at a point due to a point charge, we can use Coulomb's Law.
Coulomb's Law states that the magnitude of the electric field vector, E, created by a point charge, Q, at a distance, r, from the point charge is given by the equation:
E = k * |Q| / r^2
where k is the electrostatic constant, k = 9 x 10^9 Nm^2/C^2.
Let's calculate the magnitude of the electric field at a point 20 cm (or 0.20 m) from the point charge.
1. Convert the distance to meters:
r = 0.20 m
2. Substitute the values into the formula:
E = (9 x 10^9 Nm^2/C^2) * |-2 x 10^-6 C| / (0.20^2 m^2)
E = (9 x 10^9 Nm^2/C^2) * (2 x 10^-6 C) / (0.04 m^2)
E = (9 x 2 / 0.04) x 10^3 N/C
E = 450 x 10^3 N/C = 4.5 x 10^5 N/C
The magnitude of the electric field is 4.5 x 10^5 N/C at a point 20 cm from the point charge.
To determine the direction of the electric field, we need to consider the sign of the charge. In this case, the charge is negative, so the electric field will point radially inward towards the charge.
Therefore, the direction of the electric field at this point is inward towards the point charge.