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Chapter 2: Q59P (page 112)

Prove or disprove (with a counterexample) the following

Theorem:Suppose a conductor carrying a net charge Q,when placed in an

external electric field E→e ,experiences a force F→; if the external field is now

reversed ( localid="1657519836206" E→e→-E→e), the force also reverses ( localid="1657519875486" F→→-F→).

What if we stipulate that the external field isuniform?

Short Answer

Expert verified

If the external electric field near a conductor is reversed, the force on the conductor doesn't always get reversed.

Step by step solution

01

Step 1:Given data:

A conductor carrying a net charge Qis placed in an external electric field E→e.

02

Charge induction on a conductor

A charge induces opposite charge on a conductor near it.

03

A spherical conductor placed in front of a point charge

Consider a conducting sphere placed in front of a positive point charge. The point charge induces negative charge on the closest surface of the sphere. The force on the sphere is thus towards the point charge.

If the point charge is negative, the field on the sphere changes sign. This time, positive charge is induced on the closest surface. The force is thus still towards the point charge.

Thus, in this case, the change in direction of the external electric field doesn't change the direction of force on the conductor. This disproves the theorem.

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Most popular questions from this chapter

All of electrostatics follows from the 1/r2character of Coulomb's law, together with the principle of superposition. An analogous theory can therefore be constructed for Newton's law of universal gravitation. What is the gravitational energy of a sphere, of mass M and radius R, assuming the density is uniform? Use your result to estimate the gravitational energy of the sun (look up the relevant numbers). Note that the energy is negative-masses attract, whereas (like) electric charges repel. As the matter "falls in," to create the sun, its energy is converted into other forms (typically thermal), and it is subsequently released in the form of radiation. The sun radiates at a rate of3.86×1026W; if all this came from gravitational energy, how long would the sun last? [The sun is in fact much older than that, so evidently this is not the source of its power.]

A conical surface (an empty ice-cream cone) carries a uniform surface charge .The height of the cone is as is the radius of the top. Find the potential difference between points (the vertex) and (the center of the top).

Suppose an electric field E(x.y,z)has the form

Ex=ax,Ey=0,Ez=0

Where ais a constant. What is the charge density? How do you account for the fact that the field points in a particular direction, when the charge density is uniform?

Calculate the divergence of the following vector functions:

Two spheres, each of radius R and carrying uniform volume charge densities +p and -p , respectively, are placed so that they partially overlap (Fig. 2.28). Call the vector from the positive center to the negative center d. Show that the field in the region of overlap is constant, and find its value. [Hint: Use the answer to Prob. 2.12.]

A sphere of radius Rcarries a charge density ρ(r)=kr(where kis a constant). Find the energy of the configuration. Check your answer by calculating it in at least two different ways.
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