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Chapter 18: Q37 P (page 759)

A Nichrome wire 30 cm long and 0.25 mm in diameter is connected to a 1.5 V flashlight battery. What is the electric field inside the wire? Why you don’t have to know how the wire is bent? How would your answer change if the wire diameter change were 0.35 mm? (Not that the electric field in the wire is quiet small compared to the electric field near a charged tape.)

Short Answer

Expert verified

The electric field inside the wire is 5V/m and it remains same for new wire diameter.

Step by step solution

01

Identification of given data

The emf of the flashlight battery is ε=1.5V

The length of Nichrome wire is l=30cm

The diameter of wire is d=0.25mm

The new diameter of wire is D=0.35mm
The amount of charge at the positive end of battery plate is found by the product of the capacitance and emf of the battery.

02

Determination of electric field inside the wire

The electric field inside the wire is given as:

E=Vl

Substitute all the values in above equation.

E=1.5V30cm1m100cmE=5V/m

The electric field does not change with the diameter of the wire because the length of wire and emf of flashlight battery is constant.

Therefore, the electric field inside the wire is 5V/m and it remains same for new wire diameter.

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Most popular questions from this chapter

Describe the following attributes of a metal wire in steady

state vs. equilibrium:

Metal Wire

Steady-state

Equilibrium

Location of excess charge

Motion of mobile electrons

inside the metal wire

A Nichrome wire 48 cm long and 0.25 mm in diameter is connected to a 1.6 V flashlight battery. What is the electric field inside the wire? Why you don’t have to know how the wire is bent? How would your answer change if the wire diameter change were 0.20 mm? (Not that the electric field in the wire is quiet small compared to the electric field near a charged tape.)

In the few nanoseconds before the steady state is established in a circuit consisting of a battery, copper wires, and a single bulb, is the current the same everywhere in the circuit? Explain.

Question: A circuit is constructed from two batteries and two wires, as shown in Figure 18.104. Each battery has an emf of 1.3V. Each wire is26cmlong and has a diameter of 7×10-4m. The wires are made of a metal that has7×1028mobile electrons per cubic meter; the electron mobility is 5×10-5(m/s)/(V/m). A steady current runs through the circuit. The locations marked by ×and labeled by a letter are in the interior of the wire. (a) Which of these statements about the electric field in the interior of the wires, at the locations marked by ×'s, are true? List all that apply. (1) The magnitude of the electric field at location G is larger than the magnitude of the electric field at location F. (2) At every marked location the magnitude of the electric field is the same. (3) At location B the electric field points to the left. (b) Write a correct energy conservation (round-trip potential difference) equation for this circuit, along a round-trip path starting at the negative end of battery 1 and traveling counterclockwise through the circuit (that is, traveling to the left through the battery, and continuing on around the circuit in the same direction). (c) What is the magnitude of the electric field at location B? (d) How many electrons per second enter the positive end of battery 2? (e)If the cross-sectional area of both wires were increased by a factor of 2, what would be the magnitude of the electric field at location B? (f) Which of the diagrams in Figure 18.105 best shows the approximate distribution of excess charge on the surface of the circuit?

In the circuit shown in Figure 18.110, the two thick wires and the thin wire are made of Nichrome.

(a) Show the steady-state electric field at indicated locations, including in the thin wire. (b) Carefully draw pluses and minuses on your own diagram to show the approximate surface-charge distribution in the steady state. Make your drawing show the differences between regions of high surface-charge density and regions of low surface-charge density. (c) The emf of the battery is1.5V. In Nichrome, there are n=9×1028 mobile electrons per m3, and the mobility of mobile electrons is μ=7×10-5(m/s)(V/m). Each thick wire has a length of L1 =20cm=0.2m and a cross-sectional area of A1 =9×10-8 m2. The thin wire has a length of L2=5cm=0.05m and a cross-sectional area of A2=1.5×10-8m2. (The total length of the three wires is 45cm)Calculate the number of electrons entering the thin wire every second in the steady state. Do not make any approximations, and do not use Ohm’s law or series-resistance equations. State briefly where each of your equations comes from.
See all solutions

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