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Chapter 2: Q11CP (page 45)

Figure 16.60 shows a portion of a long, negatively charged rod. You need to calculate the potential difference VD-Vc.

(a) What is the direction of the path (+yor-y)?

(b) What is the sign ofVA-VB?

Short Answer

Expert verified

a). The potential difference is a property of Egenerated by the source charges. It is independent of the sign or magnitude of the test charge.

b). VA-VB, The direction of the path is along the -y direction.

Step by step solution

01

Direction of the path.

The potential difference is a property ofE generated by the source charges. It is independent of the sign or magnitude of the test charge. The sign of the potential differenceVA-VB due to the rod does not depend on the sign of the test charge.

02

Sign of VA-VB.

Since to determine, VA-VB, Ais the final point and B is the initial point, so the path is from BtoA.

Notice that with the source charge on the rod being negative, it generates a downward electric field. By inspection the vector Eis parallel to the path,

So,□V=VA-VB<0.

Hence, the direction of the path is along the -y direction.

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