Chapter 26: Q. 3 (page 736)

a. Suppose that $\vec{E} = \vec{0} V / m$ throughout some region of space. Can you conclude that $V = 0 V$ in this region? Explain.
b. Suppose that $V = 0 V$ throughout some region of space. Can you conclude that $\vec{E} = \vec{0} V / m$ in this region? Explain.

Short Answer

Expert verified

(a) No, $v$ is not necessarily $0$ .

(b) Yes, $\vec{| E |}$ is zero

Step by step solution

Given information and formula used

Given :

a. $\vec{E} = \vec{0} V / m$

b. $V = 0 V$

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 (“derivative” or “gradient”) of the potential.

$\vec{E} = - \frac{Δ V}{Δ x}$

Determining if V = 0 Vin this region

a) No.

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

Determining if E→= 0→ V/m

(b) The answer is yes.

Because $\vec{E} = - \frac{Δ V}{Δ x}$ , when $V$ is constant in a region of space, $E = 0 V / m$ .

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a. Suppose that $\vec{E} = \vec{0} V / m$ throughout some region of space. Can you conclude that $V = 0 V$ in this region? Explain.
b. Suppose that $V = 0 V$ throughout some region of space. Can you conclude that $\vec{E} = \vec{0} V / m$ in this region? Explain.

Short Answer

Step by step solution

Given information and formula used

Determining if V = 0 Vin this region

Determining if E→= 0→ V/m

One App. One Place for Learning.

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a. Suppose that E→=0→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→=0→V/m in this region? Explain.

Short Answer

Step by step solution

Given information and formula used

Determining if V = 0 Vin this region

Determining if E→= 0→ V/m

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Nuclear Physics

Astrophysics

Scientific Method Physics

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Fields in Physics

Study anywhere. Anytime. Across all devices.

a. Suppose that $\vec{E} = \vec{0} V / m$ throughout some region of space. Can you conclude that $V = 0 V$ in this region? Explain.
b. Suppose that $V = 0 V$ throughout some region of space. Can you conclude that $\vec{E} = \vec{0} V / m$ in this region? Explain.