PHYS 2212 Module 2.4

Conductors in Electrostatic Equilibrium

Recommended Reading

2.4 Conductors in Electrostatic Equilibrium

Learning Objectives

By the end of this section, you will be able to:

  • Describe the electric field within a conductor at equilibrium
  • Describe the electric field immediately outside the surface of a charged conductor at equilibrium
  • Explain why if the field is not as described in the first two objectives, the conductor is not at equilibrium

Gauss’s Law and Conductors

Practice!

Practice 2.4.1
A metal conducting sphere of radius R holds a total charge Q. What is the surface charge density, , on the outer surface of the conducting sphere?
A.
B.
C.
D.
E.
Check your answer: B
Practice 2.4.2
A metal conducting sphere of radius R holds a total charge Q. What is the charge enclosed by a Gaussian sphere of radius r, where 0 < r < R?
A.
B.
C.
D.
E.
Check your answer: E
Practice 2.4.3
A metal conducting sphere of radius R holds a total charge Q. What is the magnitude of the electric field produced by the charged sphere inside the sphere at a radial distance r from the sphere’s center, where 0 < r < R?
A.
B.
C.
D.
E.
Check your answer: A
Practice 2.4.4

A point charge with magnitude +Q is located inside the cavity of a spherical conducting shell. The shell has an inner radius equal to a, an outer radius equal to b, and holds a net charge of -3Q, as shown in the figure. What is the surface charge density, , on the inner surface of the conducting shell?
A.
B.
C.
D.
E.
Check your answer: B
Practice 2.4.5

A point charge with magnitude +Q is located inside the cavity of a spherical conducting shell. The shell has an inner radius equal to a, an outer radius equal to b, and holds a net charge of -3Q, as shown in the figure. What is the surface charge density, , on the outer surface of the conducting shell?
A.
B.
C.
D.
E.
Check your answer: E
Practice 2.4.6

A point charge with magnitude +Q is located inside the cavity of a spherical conducting shell. The shell has an inner radius equal to a, an outer radius equal to b, and holds a net charge of -3Q, as shown in the figure. What is the magnitude of the electric field inside the conducting shell, at a radial distance r where a < r < b?
A.
B.
C.
D.
E.
Check your answer: D
Practice 2.4.7

A point charge with magnitude +Q is located inside the cavity of a spherical conducting shell. The shell has an inner radius equal to a, an outer radius equal to b, and holds a net charge of -3Q, as shown in the figure. What is the magnitude of the electric field outside the conducting shell, at a radial distance r where r > b?
A.
B.
C.
D.
E.
Check your answer: C

Discuss!

Reflect on these questions and take notes on how you would answer them. Then we will share these thoughts together in a class discussion.

A charge −2Q is brought near a conducting sphere.

What is the electric field in the region r < Ra (inside the cavity of the conducting sphere)?

A ball with charge −50e lies at the center of a hollow spherical metal shell that has a net charge of −100e.

What are the charges on the shell’s inner surface and outer surface, respectively?

A ball with charge −50e lies off-center inside a hollow spherical metal shell that has a net charge of −100e.

What are the charges on the shell’s inner surface and outer surface, respectively?

A positive charge +Q is kept fixed at the center of a spherical neutral conducting shell. An object with negative charge −Q is brought near the outside of the sphere.

Which picture best represents the charge distributions?