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Chapter 18: Problem 35

Refer to Problem \(34 .\) With the copper wire connected to an ideal battery, the current increases greatly when the wire is immersed in liquid nitrogen. Ignoring changes in the wire's dimensions, state whether each of the following quantities increases, decreases, or stays the same as the wire is cooled: the electric field in the wire, the resistivity, and the drift speed. Explain your answers.

Short Answer

Expert verified
Answer: The electric field in the wire remains the same, the resistivity decreases, and the drift speed increases.

Step by step solution

01

Electric Field in the Wire

The electric field in the wire is given by E=V/L, where V is the voltage across the wire, and L is the length of the wire. With the copper wire connected to an ideal battery, the voltage V remains constant. As the length L of the wire is also unchanged when immersing it in liquid nitrogen, the electric field (E) in the wire will stay the same.
02

Resistivity

Resistivity of a conductor depends on its temperature. As the temperature decreases, the resistivity of the conductor also decreases. When the copper wire is immersed in liquid nitrogen, the temperature is significantly lowered, which causes a decrease in resistivity.
03

Current

With a decreased resistivity and a constant electric field, we can use Ohm's law to find that the current (I) flowing through the wire will increase. Ohm's law states that I = E/R, where R is the resistance (which is related to resistivity). Since E is constant and the resistivity (and therefore resistance) has decreased, the current I must increase.
04

Drift Speed

Drift speed (v_d) is the average velocity at which the charge carriers move in response to an electric field. It can be related to the current using the equation I = nAv_dq, where n is the number density of charge carriers, A is the cross-sectional area of the wire, and q is the charge of an electron. Since the cross-sectional area, number density of charge carriers, and charge of an electron all remain constant, the increased current (I) will cause the drift speed (v_d) to increase as well. In conclusion, as the wire is cooled by immersing it in liquid nitrogen, the electric field in the wire stays the same, the resistivity decreases, and the drift speed increases.

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