Final answer:
To calculate the current carried by a gold wire with a diameter of 0.86 mm and an electric field of 0.49 V/m, we first find the resistance using the resistivity formula with the wire's cross-sectional area. Then we apply Ohm's Law to find the current, considering the relationship between electric field, voltage, and resistance.
Step-by-step explanation:
To calculate the current carried by the gold wire, we can use Ohm's Law, which relates current I, voltage V, and resistance R. The resistance can be determined by using the resistivity formula R = ρL/A, where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.
First, calculate the cross-sectional area A of the wire using the formula A = π(d/2)^2, where d is the diameter of the wire. Since the diameter of the wire is 0.86 mm, we must convert this to meters before calculating the area. The area A in square meters is thus π(0.86 × 10^{-3} / 2)^2.
Using the given electric field E = 0.49 V/m and the formula V = E × L, we find the voltage V across a length L of the wire. However, the length L cancels out when we use Ohm's law, since R = ρL/A and V = EL. The current I can then be calculated using I = V/R.
Substituting the known values into Ohm's law and solving for current I gives us the current carried by the wire. This requires performing some algebraic manipulations to isolate I, and then plugging in numerical values to compute the answer.