A spherical conducting shell has a charge of -14 pCon its outer surface and a charged particle in its hollow. If the net charge on the shell is-10μC, what is the charge

(a) on the inner surface of the shell and

(b) of the particle?

Short Answer

Expert verified
  1. The charge on the inner surface of the shell is +4μC.
  2. The charge of the particle is -4μC.

Step by step solution

01

The given data

  1. A spherical conducting shell has a charge ofqout=-14μCon its outer surface.
  2. The net charge on the shell is Q=-10μC.
02

Understanding the concept of the electric field

Using the concept of the Gaussian surface, we can calculate the required charge on a body. Consider the given shell as a Gaussian surface, and then some amount of charge remains at the inner surface while some at the outer surface.

Hence, using this concept, the net charge on the shell is the total value of all charges on the shell.

Formula:

Let,qinbe the charge on the inner surface andqoutthe charge on the outer surface. The net charge on the shell is given as:

Q=qin+qout (i)

03

a) Calculation of the charge on the inner surface of the shell

Using the given data in equation (i), the charge on the inner surface of the shell is given as:

qin=-10μC-(-14μC)=+4μC

Hence, the value of the charge is +4μC.

04

b) Calculation of the charge of the particle

Let q be the charge of the particle. In order to cancel the electric field inside the conducting material, the contribution from the in qin=+4μCon the inner surface must be canceled by that of the charged particle in the hollow. That is, the enclosed charge in the shell surface should be:

qenc=q-qi=0

Thus, the particle’s charge is given as:

q=-qin=-4μC

Hence, the value of the charge is -4μC.

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Most popular questions from this chapter

The electric field in a certain region of Earth’s atmosphere is directed vertically down. At an altitude of 300 mthe field has magnitude60.0 N/C; at an altitude of200m, the magnitude is . Find the net amount of charge contained in a cube 100 m on edge, with horizontal faces at altitudes of200 and 300m.

Charge is distributed uniformly throughout the volume of an infinitely long solid cylinder of radius R.

(a) Show that, at a distance r < R from the cylinder axis,E=pr2ε0where is the volume charge density.

(b) Write an expression for E when r > R.

The electric field at point Pjust outside the outer surface of a hollow spherical conductor of inner radius 10 cmand outer radius 20 cmhas magnitude 450 N/ Cand is directed outward. When a particle of unknown charge Qis introduced into the center of the sphere, the electric field at Pis still directed outward but is now 180 N/C.

(a) What was the net charge enclosed by the outer surface before Qwas introduced?

(b) What is charge Q?

After Qis introduced, what is the charge on the

(c) inner and

(d) outer surface of the conductor?

Rank the situations of Question 9 according to the magnitude of the electric field

(a) halfway through the shell and

(b) at a point 2R from the center of the shell, greatest first.

Figure 23-52 gives the magnitude of the electric field inside and outside a sphere with a positive charge distributed uniformly throughout its volume. The scale of the vertical axis is set by Es=5.0×10N/C. What is the charge on the sphere?

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