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Chapter 24: Q14P (page 710)

Consider a particle with charge q = 1.0 mC, point Aat distance d1 = 2.0 mfrom q, and point Bat distance d2 = 1.0 m. (a) If Aand B are diametrically opposite each other, as in Fig. 24-36a, what is the electric potential difference VA - VB? (b) What is that electric potential difference if Aand Bare located as in Fig. 24-36b?

Short Answer

Expert verified
  1. The potential difference is, -4.5脳103V.
  2. V (r) depends only on the magnitude of r, the outcome remains the same.

Step by step solution

01

Given

  • The charge on the particle is, q=1.0渭C.
  • The distance between point A and charge q is, d1 = 2.0m.
  • The distance between point B and charge q is, d2 = 1.0m.
02

Understanding the concept

The electric potential V at the surface of a drop of charge q and radius R is given by

V=q4蟺蔚0R

Using this equation, we find potential differences between two points.

03

(a) Calculate the electric potential difference VA - VB if A and B are diametrically opposite each other

The potential difference is expressed as,

VA-VB=q4蟺蔚0rA-q4蟺蔚0rB

Substitute all the value in the above equation.

VA-VB=q4蟺蔚0rA-q4蟺蔚0rBVA-VB=1.0脳10-6C8.99脳109N.m2/C212.0m-11.0m=-4.5脳103V

Hence the potential difference is, -4.5脳103V.

04

(b) Calculate electric potential difference if A and B are located as in figure

Since V (r) depends only on the magnitude of r, the outcome remains the same.

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Most popular questions from this chapter

(a) Using Eq. 24-32, show that the electric potential at a point on the central axis of a thin ring (of charge q and radius R ) and at distance Z from the ring is,V=14蟺蔚o鈰�qR2+z2

(b) From this result, derive an expression for the electric field magnitude

E at points on the ring鈥檚 axis; compare your result with the calculation of E in Module 22-4.

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.)

Question: Two particles of chargesq1and q2 , are separated by distance in Fig. 24-40. The net electric field due to the particles is zero at x = d/4 .With V = 0 at infinity, locate (in terms of ) any point on the x-axis (other than at infinity) at which the electric potential due to the two particles is zero.

In Fig. 24-31a, what is the potential at point P due to charge Q at distance R from P? Set at infinity. (b) In Fig. 24-31b, the same charge has been spread uniformly over a circular arc of radius R and central angle 40. What is the potential at point P, the center of curvature of the arc? (c) In Fig. 24-31c, the same charge Q has been spread uniformly over a circle of radius R . What is the potential at point P , the center of the circle? (d) Rank the three situations according to the magnitude of the electric field that is set up at P, greatest first.

A plastic rod has been bent into a circle of radius R = 8.20 cm. It has a charge Q1 = +4.20pCuniformly distributed along one-quarter of its circumference and a charge Q2 = -6Q1uniformly distributed along the rest of the circumference (Fig. 24-44). With V = 0at infinity, what is the electric potential at (a) the center Cof the circle and (b) point P, on the central axis of the circle at distance D = 6.71cmfrom the center?
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