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Chapter 26: Q. 3 (page 736)

a. Suppose that E鈫�=0鈫�V/mthroughout some region of space. Can you conclude that V=0Vin this region? Explain.

b. Suppose that V=0V throughout some region of space. Can you conclude that E鈫�=0鈫�V/m in this region? Explain.

Short Answer

Expert verified

(a) No, vis not necessarily 0.

(b) Yes, |E|鈫�is zero

Step by step solution

01

Given information and formula used  

Given :

a. E鈫�=0鈫�V/m

b. V=0V

Theory used :

In the region of constant electric potential, electric field is zero so there is no charge inside the region.

Electric field is the negative slope (鈥渄erivative鈥� or 鈥済radient鈥�) of the potential.

E鈫�=鈭�螖V螖x

02

Determining if  V = 0 Vin this region 

a) No.

However, you can deduce that 鈭�V=0V, implying that the potential in that region of space is constant.

03

Determining if E→= 0→ V/m

(b) The answer is yes.

Because E鈫�=鈭�螖V螖x, when Vis constant in a region of space, E=0V/m.

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Most popular questions from this chapter

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