Final answer:
To find the magnitude of the electric field in the aluminum wire carrying a current of 0.450 A, we can use Ohm's Law and calculate the resistance using the resistivity, length, and cross-sectional area of the wire. Once we have the resistance, we can find the voltage and use it to determine the electric field.
Step-by-step explanation:
To find the magnitude of the electric field (E) in the wire, you can use Ohm's Law, which is given by the equation:
V=I⋅R
where:
V is the voltage (electric potential),
I is the current,
R is the resistance.
The resistance (R) of the wire can be calculated using the formula:
R=ρ⋅ L/A
where:
ρ is the resistivity of the material (given as 2.82×10−8 Ω⋅m for aluminum),
L is the length of the wire,
A is the cross-sectional area of the wire.
The cross-sectional area (A) of the wire can be found using the formula for the area of a circle:
A=π⋅r2
where:
r is the radius of the wire, and r= d/2 .
The temperature coefficient of resistivity (α) is given as 3.90×10−3 °C −1, and the change in resistance (ΔR) due to a change in temperature (ΔT) is given by:
ΔR=R0 ⋅α⋅ΔT
where:
R0 is the initial resistance,
α is the temperature coefficient of resistivity,
ΔT is the change in temperature.
Now, let's go step by step:
Calculate the initial resistance (R0):
R0 = ρ⋅ L/A0
Calculate the change in resistance (ΔR) due to the change in temperature:
ΔR=R0⋅α⋅ΔT
Find the new resistance (R) at the given temperature:
R=R0+ΔR
Use Ohm's Law to find the voltage (V):
V=I⋅R
Calculate the electric field (E):
E= V/L
Let's proceed with the calculations. For simplicity, let's assume that the change in temperature (ΔT) is zero (initial temperature is given as 20.0 ∘C), so the change in resistance (ΔR) is zero. If the temperature is different, you'll need to incorporate the temperature change in the calculations.