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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’s center of curvature is at the origin and its radius R is 2. 00 m; the angle indicated isθ=20.0°.

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,θ=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=14πε0QR (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=14πε0Q1R+14πε0Q22R+14πε0Q3R=14πε0×Q1R1+42-2=9.0×109×7.21×10-122.0=32.44×10-3V=32.4mV

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

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Most popular questions from this chapter

Question: The electric potential at points in an x-yplane is given byv=(2.0V/m2)x2-(3.0V/m2)y2. In unit-vector notation, what is the electric field at the point (role="math" localid="1662092062999" 3.0m,2.0m)?

A graph of the x component of the electric field as a function of x in a region of space is shown in Fig. 24-35. The scale of the vertical axis is set by Exs = 20.0 N/C. The y and z components of the electric field are zero in this region. If the electric potential at the origin is 10 V, (a) what is the electric potential at x = 2.0 m, (b) what is the greatest positive value of the electric potential for points on the x axis for which 0≤x≤6.0m, and (c) for what value of x is the electric potential zero?

The thin plastic rod of length L = 10.0cmin Fig. 24-47 has a non-uniform linear charge densityλ=cx, wherec=49.9pC/m2. (a) With V= 0 at infinity, find the electric potential at point P2 on the yaxis at y = D = 3.56cm. (b) Find the electric field component at P2. (c) Why cannot the field component Exat P2 be found using the result of (a)?

Here are the charges and coordinates of two charged particles located in an xyplane:q2'=-3.0×10-6C,x=+3.50cm,y=+0.500cmandrole="math" localid="1662728679285" q2=-4.0×10-6C,x=-2.00cm,y=+1.50cm. How much work must be done to locate these charges at their given positions, starting from infinite separation?

(a) Figure 24-42ashows a non-conducting rod of length L = 6.00cmand uniform linear charge density λ=(3.68pC/m). Assume that the electric potential is defined to be V = 0at infinity. What is Vat point Pat distance d = 8.00cmalong the rod’s perpendicular bisector? (b) Figure 24-42bshows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 3.68pC/m. With V = 0at infinity, what is the net electric potential at the

VatP?
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