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Chapter 26: Q. 3 (page 736)

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

Expert verified

(a) No, vis not necessarily 0.

(b) Yes, |E|→is zero

Step by step solution

01

Given information and formula used  

Given :

a. E→=0→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 (“derivative” or “gradient”) of the potential.

E→=−ΔVΔx

02

Determining if  V = 0 Vin this region 

a) No.

However, you can deduce that ∆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→=−ΔVΔx, when Vis constant in a region of space, E=0V/m.

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Most popular questions from this chapter

The electric potential in a region of space is V=(150x2-200y2)V, where xand yare in meters. What are the strength and direction of the electric field at (x,y)=(2.0m,2.0m)? Give the direction as an angle cwor ccw(specify which) from the positive x-axis

High-frequency signals are often transmitted along a coaxial cable, such as the one shown in FIGURE P26.66. For example, the cable TV hookup coming into your home is a coaxial cable. The signal is carried on a wire of radius R1while the outer conductor of radius R2is grounded (i.e., at V=0V). An insulating material fills the space between them, and an insulating plastic coating goes around the outside.

a. Find an expression for the capacitance per meter of a coaxial cable. Assume that the insulating material between the cylinders is air.

b. Evaluate the capacitance per meter of a cable having R1=0.50mmand R2=3.0mm.

Each capacitor in FIGURE CP26.83 has capacitance C. What is the equivalent capacitance between points aand b?

Find expressions for the equivalent capacitance of

(a) Nidentical capacitors Cin parallel and

(b) Nidentical capacitors Cin series.

Two 10-cm-diameter electrodes 0.50 cm apart form a parallelplate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. What are the charge on each electrode, the electric field strength inside the capacitor, and the potential difference between the electrodes a. While the capacitor is attached to the battery? b. After insulating handles are used to pull the electrodes away from each other until they are 1.0 cm apart? The electrodes remain connected to the battery during this process. c. After the original electrodes (not the modified electrodes of part b) are expanded until they are 20 cm in diameter while remaining connected to the battery?
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