Question

In the circuit shown in Figure 18.91, all of the wire is made of Nichrome, but one segment has a much smaller cross-sectional area. On a copy of this diagram, using the same scale for magnitude that you used in the previous question for Figure 18.90, show the steady-state electric field at the locations indicated, including in the thinner segment. Before attempting to answer these 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. Use the same scale for magnitude as you did in the previous question.

(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 a large gradient of surface charge on the wire between locations Cand E. (2) The electron current is the same at every location in this circuit.

(3) Fewer electrons per second pass location Ethan location C.

(4) The magnitude of the electric field at location Gis smaller in this circuit than it

was in the previous circuit (Figure 18.90).

(5) The magnitude of the electric field is the same at every location in this circuit.

(6) The magnitude of the electric field at location D is larger than the magnitude of the electric field at location G.

(7) There is no surface charge at all on the wire near location G.

(8) The electron current in this circuit is less than the electron current in the previous circuit (Figure 18.90).

Short answer

(a) The direction of electric field in the circuit is as follows:

Step-by-step solution

Given data

A steady-state current flows through the Nichrome wire in the circuit, with one segment having a much smaller cross-sectional area

The following statements are provided:

(1) There is a large gradient of surface charge on the wire between locations Cand E.

(2) The electron current is the same at every location in this circuit.

(3) Fewer electrons per second pass location Ethan location C.

(4) The magnitude of the electric field at location Gis smaller in this circuit than it

was in the previous circuit (Figure 18.90).

(5) The magnitude of the electric field is the same at every location in this circuit.

(6) The magnitude of the electric field at location D is larger than the magnitude of the electric field at location G.

(7) There is no surface charge at all on the wire near location G.

(8) The electron current in this circuit is less than the electron current in the previous circuit (Figure 18.90).

Electric field direction

Electric field always points from the positive terminal to the negative terminal of a battery.

(a) Determination of electric field in the circuit

At steady state, the electric field is uniform for all identical locations of the wire in a circuit and is directed from the positive to the negative terminal. Since the current is kept uniform, the field is larger in the narrower section as current is directly proportional to both the cross sectional area and electric field. This is depicted in the following diagram: