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Chapter 24: Q73P (page 715)

(a) If an isolated conducting sphere10 cmin radius has a net charge of4.0μCand ifV=0at infinity, what is the potential on the surface of the sphere? (b) Can this situation actually occur, given that the air around the sphere undergoes electrical breakdown when the field exceeds3.0MV/m?

Short Answer

Expert verified

a) The potential on the surface of the sphere is, 3.6×105 V.

b) The situation is not possible

Step by step solution

01

Step 1: Identification of the given data

For the isolated conducting sphere

Its radius r=10 cmand its charge q=4.0μC, V=0at infinity.

02

Understanding the concept

Electric Potential is given by,V=14πεo·qr

03

(a) Calculate the potential on the surface of the sphere

The electric potential is expressed as,

V=14πεo·qr

Substitute all the value in the above equation.

V=9.0×109N.m2/C2×4.0×10-6 C0.10 mV=3.6×105 V

Hence the potential on the surface of the sphere is, 3.6×105 V.

04

(b) Find out if this situation canactually occur, given that the air around the sphere undergoes electrical breakdown when the field exceeds 3.0MV/m

The field just outside the sphere is expressed as,

E=14πεo·qr2E=Vr

Substitute all the value in the above equation.

E=3.6×105 V0.10 m=3.6×106V/m

Hence the value is exceeds3.0MV/m, so this situation cannot occur.

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Most popular questions from this chapter

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.

Suppose Nelectrons can be placed in either of two configurations. In configuration 1, they are all placed on the circumference of a narrow ring of radius Rand are uniformly distributed so that the distance between adjacent electrons is the same everywhere. In configuration 2, N-1electrons are uniformly

distributed on the ring and one electron is placed in the center of the ring. (a) What is the smallest value of Nfor which the second configuration is less energetic than the first? (b) For that value of N, consider any one circumference electron—call it eo. How many other circumference electrons are closer to eothan the central electron is?

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°.

In the situation of Question 7, is the work done by your force positive, negative, or zero if the particle is moved (a) from Ato B, (b) from Ato C, and (c) from Bto D? (d) Rank those moves according to the magnitude of the work done by your force, greatest first.

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?
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