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Chapter 16: Q11Q (page 662)

Figure 16.60 shows a portion of a long, negatively charged rod. You need to calculate the potential differenceVA-VB.

(a) What is the direction of the path (+y or −y)? (b) What is the sign of VA-VB?

Short Answer

Expert verified

a) The direction of path is negative y-direction.

b) The sign of the potential difference is negative.

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The charge on the rod is, -q
  • The potential difference is,VA-VB
02

Concept/Significance of the electric potential.

The effort done by the field in moving unit positive charge from the reference point to the place where potential is to be found determines electric potential at any point in the field.

03

(a) Determination of the direction of the path +y or -y

The potential difference can be determined by going from point B to A which is from positive y-direction towards the negative y-direction.

Thus, the direction of path is negative y-direction.

04

(b) Determination of the sign of VA-VB.

The positive side point B has higher potential energy than the negative side point A. So, the potential difference∆V=VA-VB is negative.

Thus, the sign of the potential difference is negative.

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Most popular questions from this chapter

A thin spherical shell of radius \({R_1}\)made of plastic carries a uniformly distributed negative charge \( - {Q_1}\). A thin spherical shell of radius \({R_2}\)made of glass carries a uniformly distributed positive charge \( + {Q_2}\). The distance between centers is \(L\), as shown in Figure 16.80. (a) Find the potential difference \({V_B} - {V_A}\). Location A is at the center of the glass sphere, and location \(B\) is just outside the glass sphere. (b) Find the potential difference \({V_C} - {V_B}\). Location \(B\) is just outside the glass sphere, and location \(C\) is a distance d to the right of \(B\). (c) Suppose the glass shell is replaced by a solid metal sphere with radius R2 carrying charge \( + {Q_2}\). Would the magnitude of the potential difference \({V_B} - {V_A}\) be greater than, less than, or the same as it was with the glass shell in place? Explain briefly, including an appropriate physics diagram.

What is the maximum possible potential (relative to infinity) of the metal sphere of 10-cm radius? What is the maximum possible potential (relative to infinity) of the metal sphere of only 1-mm radius? These results hint at the reason why a highly charged piece of metal (with uniform potential throughout) tends to spark at places where the radius of curvature is small or at places where there are sharp points. Remember that breakdown electric strength for air is roughly\[{\bf{3 \times 1}}{{\bf{0}}^{\bf{6}}}\;\frac{{\bf{V}}}{{\bf{m}}}\].

long thin metal wire with radius rand lengthLis surrounded by a concentric long narrow metal tube of radius R, whereR>>L, as shown in Figure 16.86. Insulating spokes hold the wire in the center of the tube and prevent electrical contact between the wire and the tube. A variable power supply is connected to the device as shown. There is a charge+Qon the inner wire and a charge−Qon the outer tube. As we will see when we study Gauss’s law in a later chapter, the electric field inside the tube is contributed solely by the wire, and the field outside the wire is the same as though the wire were infinitely thin; the outer tube does not contribute as long as we are not near the ends of the tube. (a) In terms of the chargeQ, lengthL, inner radiusr, and outer radiusR , what is the potential differenceVtube−Vwire between the inner wire and the outer tube? Explain, and include checks on your answer. (b) The power-supply voltage is slowly increased until you see a glow in the air very near the inner wire. Calculate this power-supply voltage (give a numerical value), and explain your calculation. The lengthL=80 cm , the inner radiusr=0.7 mm, and the outer radiusR=3 cm. This device is called a “Geiger–Müller tube” and was one of the first electronic particle detectors. The voltage is set just below the threshold for making the air glow near the wire. A charged particle that passes near the center wire can trigger breakdown in the air, leading to a large current that can be easily measured.

Question: In a circuit there is a copper wire 40 cm long with a potential difference from one end to the other end of . What is the magnitude of electric field inside the wire?

Suppose that the potential difference in going from location (2.00,3.50,4.00)m to locationrole="math" localid="1657094482453" (2.00,3.52,4.00)m is3V. What is the approximate value ofEyin this region? Include the appropriate sign.
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