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Chapter 22: Problem 10

Which of the following statements is (are) true? a) There will be no change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed on the outer surface. b) There will be some change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed on the outer surface. c) There will be no change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed at the center of the sphere. d) There will be some change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed at the center of the sphere.

Short Answer

Expert verified
a) Placing additional charge on the outer surface of the sphere will not change the charge on the inner surface. b) Placing additional charge on the outer surface of the sphere will change the charge on the inner surface. c) Placing additional charge at the center of the sphere will not change the charge on the inner surface. d) Placing additional charge at the center of the sphere will change the charge on the inner surface. Answer: a) and c)

Step by step solution

01

Statement a: Additional outer charge and no change in the inner surface charge

If additional charge is placed on the outer surface of a hollow conducting sphere, the charges will redistribute on the outer surface to maintain a zero electric field inside the sphere. The inner surface remains at zero electric field, so there is no change in the charge on the inner surface. Therefore, statement a is true.
02

Statement b: Additional outer charge and change in the inner surface charge

This statement is the opposite of statement a. Since we have already concluded that there will be no change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed on the outer surface, statement b is false.
03

Statement c: Additional central charge and no change in the inner surface charge

If additional charge is placed at the center of a hollow conducting sphere, the electric field inside the sphere will be nonzero. To maintain a zero electric field in the conductor, the charges on the inner surface of the sphere will redistribute to cancel the field created by the central charge. This redistribution causes no change in the total charge on the inner surface, so statement c is true.
04

Statement d: Additional central charge and change in the inner surface charge

This statement is the opposite of statement c. Since we have already concluded that there will be no change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed at the center of the sphere, statement d is false. Therefore, the true statements are a) and c).

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Most popular questions from this chapter

A charge per unit length \(+\lambda\) is uniformly distributed along the positive \(y\) -axis from \(y=0\) to \(y=+a\). A charge per unit length \(-\lambda\) is uniformly distributed along the negative \(y\) axis from \(y=0\) to \(y=-a\). Write an expression for the electric field (magnitude and direction) at a point on the \(x\) -axis a distance \(x\) from the origin.

Two infinite, uniformly charged, flat nonconducting surfaces are mutually perpendicular. One of the surfaces has a charge distribution of \(+30.0 \mathrm{pC} / \mathrm{m}^{2}\), and the other has a charge distribution of \(-40.0 \mathrm{pC} / \mathrm{m}^{2}\). What is the magnitude of the electric field at any point not on either surface?

A uniform sphere has a radius \(R\) and a total charge \(+Q,\) uniformly distributed throughout its volume. It is surrounded by a thick spherical shell carrying a total charge \(-Q,\) also uniformly distributed, and having an outer radius of \(2 R\). What is the electric field as a function of \(R ?\)

An electric dipole consists of two equal and opposite charges situated a very small distance from each other. When the dipole is placed in a uniform electric field, which of the following statements is true? a) The dipole will not experience any net force from the electric field; since the charges are equal and have opposite signs, the individual effects will cancel out. b) There will be no net force and no net torque acting on the dipole. c) There will be a net force but no net torque acting on the dipole. d) There will be no net force, but there will (in general) be a net torque acting on dipole.

A \(-6.00-n C\) point charge is located at the center of a conducting spherical shell. The shell has an inner radius of \(2.00 \mathrm{~m},\) an outer radius of \(4.00 \mathrm{~m},\) and a charge of \(+7.00 \mathrm{nC}\) a) What is the electric field at \(r=1.00 \mathrm{~m} ?\) b) What is the electric field at \(r=3.00 \mathrm{~m} ?\) c) What is the electric field at \(r=5.00 \mathrm{~m} ?\) d) What is the surface charge distribution, \(\sigma,\) on the outside surface of the shell?
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