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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

In Fig. 24-66, point P is at distanced1=4.00m from particle 1(q1−2e) and distanced2=2.00m from particle 2 (q2+2e), with both particles fixedin place.

(a) With V=0at infinity, what is V at P? If we bring a particle ofchargeq3+2e from infinity to P,

(b) how much work do we do and

(c) what is the potential energy of the three-particle system?

A particle of charge qis fixed at point P, and a second particle of mass mand the same charge qis initially held a distance r1 from P. The second particle is then released. Determine its speed when it is a distance from P. Letq=3.1μC,m=20μg,r1=0.90mm,r2=2.5mm.

(a) what is the electric potential energy of two electrons separated by 2.00 nm? (b) If the separation increases, does the potential energy increase or decrease?

Question: In Fig. 24-41a, a particle of elementary charge +eis initially at coordinate z = 20 nmon the dipole axis (here a zaxis) through an electric dipole, on the positive side of the dipole. (The origin of zis at the center of the dipole.) The particle is then moved along a circular path around the dipole center until it is at coordinate z = -20 nm, on the negative side of the dipole axis. Figure 24-41bgives the work done by the force moving the particle versus the angle u that locates the particle relative to the positive direction of the z-axis. The scale of the vertical axis is set byWas=4.0×10-30J.What is the magnitude of the dipole moment?

Question: In Fig. 24-43, a plastic rod having a uniformly distributed charge Q = -25.6pChas been bent into a circular arc of radius R = 3.71 cmand central angleϕ=120°. With V = 0at infinity, what is the electric potential at P, the center of curvature of the rod?
See all solutions

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