Final Answer:
The electric field 5.0 cm from a very long charged wire, given that it is 200, is b) 400 N/C.
Step-by-step explanation:
The electric field (E) around a long charged wire is given by the formula E = (k ⋅ λ) / r, where k is Coulomb's constant, λ is the linear charge density, and r is the radial distance from the wire. In this scenario, with a given electric field (E = 200) and a distance (r = 5.0 cm = 0.05 m), we can rearrange the formula to find the linear charge density. Solving for λ, we get λ = E ⋅ r / k. Substituting the given values, we find λ = 200 ⋅ 0.05 / (9 ⋅ 10⁹) = 4.44 ⋅ 10⁻⁷ C/m.
Now that we have the linear charge density, we can find the electric field at 5.0 cm. Substituting λ, r, and k into the electric field formula, we get E = (9 ⋅ 10⁹ ⋅ 4.44 ⋅ 10⁻⁷) / 0.05 = 400 N/C. Therefore, the correct answer is b) 400 N/C.
In conclusion, the electric field around a charged wire is directly related to the linear charge density and the radial distance from the wire. By applying the appropriate formula and substituting the given values, we find that the electric field 5.0 cm from the wire is indeed 400 N/C.