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Chapter 18: Q39 P (page 759)

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.)

Short Answer

Expert verified

The electric field inside the wire is 3.33V/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=1.6V

The length of Nichrome wire is l=48cm

The diameter of wire is d=0.25mm

The new diameter of wire is D=0.20mm

The electric field intensity is the variation in the electric potential with distance from the charge.

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.

role="math" localid="1668586404085" E=1.6V48cm1m100cmE=3.33V/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 3.33V/m and it remains same for new wire diameter.

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Most popular questions from this chapter

Suppose that a wire leads into another, thinner wire of the same material that has only a third the cross-sectional area. In the steady state, the number of electrons per second flowing through the thick wire must be equal to the number of electrons per second flowing through the thin wire. If the drift speedV1¯in the thick wire is 4×10-5ms, what is the drift speed V¯2in the thinner wire?

In the circuit shown figure 18.108, two thick copper wires connect a 1.5 V battery to a Nichrome wire. Each thick connecting wire is 17 cm long and has a radius of 9 mm. Copper has 8.4×1028mobile electrons per cubic meter and electron mobility. The Nichrome wire is 8 cm long and has a radius of 3 mm. Nichrome has 9×1028mobile electrons per cubic meter and electron mobility of 7×10-5(ms)(Vm).

(a) What is the magnitude of the electric field in the thick copper wire?

(b) What is the magnitude of the electric field in the thin Nichrome wire?

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?

What would be the potential difference VC-VBacross the thin resistor in Figure 18.103 if the battery emf is3.5V ? Assume that the electric field in the thick wires is very small (so that the potential differences along the thick wires are negligible). Do you have enough information to determine the current in the circuit?

A steady-state current flows through the Nichrome wire in the circuit shown in Figure 18.90. Before attempting to answer the following questions, draw a copy of this diagram. All of the locations indicated by letters are inside the wire.

(a)On your diagram, show the electric field at the locations indicated, paying attention to relative magnitude.

(b)Carefully draw pluses and minuses on your diagram to show the approximate surface charge distribution that produces the electric field you drew. Make your drawing show clearly the differences between regions of high surface charge density and regions of low surface-charge density. Use your diagram to determine which of the following statements about this circuit are true.

(1) There is some excess negative charge on the surface of the wire near location B.

(2) Inside the metal wire the magnitude of the electric field is zero.

(3) The magnitude of the electric field is the same at locations Gand C.

(4) The electric field points to the left at location G.

(5) There is no excess charge on the surface of the wire.

(6) There is excess charge on the surface of the wire near the batteries but nowhere else.

(7) The magnitude of the electric field inside the wire is larger at location Gthan at location C.

(8) The electric field at location Dpoints to the left.

(9) Because the current is not changing, the circuit is in static equilibrium.
See all solutions

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