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Chapter 24: Q29P (page 711)

Question: In Fig. 24-48, what is the net electric potential at the origin due to the circular arc of charge Q1=+7.21pCand the two particles of chargesQ2=4.00Q1andQ3=-2.00Q1? The arc鈥檚 center of curvature is at the origin and its radius R is 2. 00 m; the angle indicated is胃=20.0掳.

Short Answer

Expert verified

Answer:

The net electric potential at the origin sue to the charges is 32.4 mV.

Step by step solution

01

The given data

  1. Values of the charges,Q1=+7.21pC,Q2=+4Q1andQ3=-2Q1
  2. Radius of the circular arc, R = 2m
  3. Angle indicated in the given figure,胃=200
02

Understanding the concept of the electric potential

Using the concept of the electric potential, we can get the net electric potential at the point due to charges can be calculated by adding all the potentials due to the individual charges.

Formula:

The net electric potential at the point due to a charge, V=14蟺蔚0QR (i)

03

Calculation of the net electric potential

The net potential at the origin due to the charges is given using equation (i) as follows:

Vnet=V1+V2+V3=14蟺蔚0Q1R+14蟺蔚0Q22R+14蟺蔚0Q3R=14蟺蔚0脳Q1R1+42-2=9.0脳109脳7.21脳10-122.0=32.44脳10-3V=32.4mV

Hence, the value of the electric potential is 32.4 mV.

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Most popular questions from this chapter

A thick spherical shell of charge Q and uniform volume charge density r is bounded by radiir1and r2>r1.With V=0 at infinity, find the electric potential V as a function of distance r from the center of the distribution, considering regions

(a)r>r2 ,

(b)r2>r>r1 , and

(c)r<r1 .

(d) Do these solutions agree with each other at r=r2andr=r1? (Hint: See Module 23-6.)

A positron (charge +e, mass equal to the electron mass) is moving at 1.0x107 m/sin the positive direction of an xaxis when, at x=0, it encounters an electric field directed along the xaxis. The electric potential Vassociated with the field is given in Fig. 24-57. The scale of the vertical axis is set by Vs=500.0 V. (a) Does the positron emerge from the field at x=0(which means its motion is reversed) or at x=0.50 m(which means its motion is not reversed)? (b) What is its speed when it emerges?

Figure 24-29 shows four arrangements of charged particles, all the same distance from the origin. Rank the situations according to the net electric potential at the origin, most positive first. Take the potential to be zero at infinity.

Figure 24-37 shows a rectangular array of charged particles fixed in place, with distance a = 39.0 cmand the charges shown as integer multiples of q1 = 3.40 pCand q2 = 6.00 pC. With V = 0at infinity, what is the net electric potential at the rectangle鈥檚 center? (Hint:Thoughtful examination of the arrangement can reduce the calculation.)

A non-uniform linear charge distribution given by 位=bx, where bis a constant, is located along an xaxis from x = 0to x = 0.20m. If b = 20nC/m2and V = 0at infinity, what is the electric potential at (a) the origin and (b) the point y = 0.15mon the yaxis?
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