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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

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)?

Figure 24-56ashows an electron moving along an electric dipole axis toward the negative side of the dipole. The dipole is fixed in place. The electron was initially very far from the dipole, with kinetic energy100eV. Figure 24-56bgives the kinetic energy Kof the electron versus its distance rfrom the dipole center. The scale of the horizontal axis is set byrs=0.10m.What is the magnitudeof the dipole moment?

In Fig. 24-70, point P is at the center of the rectangle. With V=0at infinity, q1=5.00fC , q2=2.00fC , q3=3.00fC, andd=2.54cm, what is the net electric potential at P due to the six charged particles?

In the rectangle of Fig. 24-55, the sides have lengths 5.0 cmand15 cm, q1= -5.0 mC, and q2= +2.0 mC. With V=0at infinity, what is the electric potential at (a) corner Aand (b) corner B? (c) How much work is required to move a charge q3= +3.0 mCfrom Bto Aalong a diagonal of the rectangle? (d) Does this work increase or decrease the electric potential energy of the three-charge system? Is more, less, or the same work required if q3 is moved along a path that is (e) inside the rectangle but not on a diagonal and (f) outside the rectangle?

Question: The ammonia molecule NH3 has a permanent electric dipole moment equal to,1.47 D where,1Debye=3.34×10-30C.m. Calculate the electric potential due to an ammonia molecule at a point 52.0nmaway along the axis of the dipole. (Set v = 0at infinity.)
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