Answer:
The closest option to the calculated electric field is 0.40 kN/C.
Step-by-step explanation:
To calculate the electric field at a point, we can use Coulomb's Law, which states that the electric field due to a point charge is given by:
E = k * (Q / r^2),
where E is the electric field, k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2), Q is the charge, and r is the distance from the point charge.
In this case, we have two charges:
Q1 = 2C at the origin (x = 0 m),
Q2 = 8C at x = 10 m,
We want to find the electric field at x = -5 m.
First, let's calculate the electric field due to Q1 at x = -5 m:
r1 = |-5 - 0| = 5 m (distance from Q1 to the point)
E1 = k * (Q1 / r1^2)
Substituting the values:
E1 = (8.99 x 10^9 Nm^2/C^2) * (2C / (5m)^2)
E1 = 8.99 x 10^9 Nm^2/C^2 * 2C / 25m^2
E1 ≈ 1.4392 x 10^8 N/C
Next, let's calculate the electric field due to Q2 at x = -5 m:
r2 = |-5 - 10| = 15 m (distance from Q2 to the point)
E2 = k * (Q2 / r2^2)
Substituting the values:
E2 = (8.99 x 10^9 Nm^2/C^2) * (8C / (15m)^2)
E2 = 8.99 x 10^9 Nm^2/C^2 * 8C / 225m^2
E2 ≈ 3.1956 x 10^7 N/C
The total electric field at x = -5 m is the sum of the electric fields due to Q1 and Q2:
E_total = E1 + E2
E_total ≈ 1.4392 x 10^8 N/C + 3.1956 x 10^7 N/C
E_total ≈ 1.7588 x 10^8 N/C
Rounding to two significant figures, the electric field at x = -5 m is approximately 1.8 x 10^8 N/C, which is equivalent to 0.18 kN/C.
Therefore, the closest option to the calculated electric field is 0.40 kN/C.