Chapter 4: Q4.14P (page 179)

When you polarize a neutral dielectric, the charge moves a bit, but the total remains zero. This fact should be reflected in the bound charges $σ_{b}$ and $ρ_{b}$ · Prove from Eqs. 4.11 and 4.12 that the total bound charge vanishes.

Short Answer

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The value of total charge of a piece of neutral dielectric $Q_{t o t a l}$ is $0$ .

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Write the given data from the question

Consider thereflected in the bound charges $σ_{b}$ and $ρ_{b}$ ·

Consider when you polarize a neutral dielectric, the charge moves a bit, but the total remains zero.

Determine the formula of total charge of a piece of neutral dielectric Qtotal.

Write the formula of total charge of a piece of neutral dielectric $Q_{t o t a l}$ .

$Q_{total} = \oint_{S} σ_{b} dS + \int_{ν} ρ_{b} d τ$ …… (1)

Here, $σ_{b}$ and $ρ_{b}$ are the reflected in the bound charges.

Determine the value of total charge of a piece of neutral dielectric Qtotal.

Determine thetotal charge of a piece of neutral dielectric.

Substitute $\vec{P} \cdot \hat{n}$ for $σ$ and $\nabla \cdot \vec{P}$ for $ρ$ into equation (1).

$Q_{t o t a l} = \oint_{S} σ d S + \int_{ν} \nabla \cdot \vec{P} d τ$

However, according to divergence law, the two terms are equivalent and cancel one another out.

$Q_{t o t a l} = 0$

Therefore, the value of total charge of a piece of neutral dielectric $Q_{t o t a l}$ is $0$ .

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When you polarize a neutral dielectric, the charge moves a bit, but the total remains zero. This fact should be reflected in the bound charges $σ_{b}$ and $ρ_{b}$ · Prove from Eqs. 4.11 and 4.12 that the total bound charge vanishes.

Short Answer

Step by step solution

Write the given data from the question

Determine the formula of total charge of a piece of neutral dielectric Qtotal.

Determine the value of total charge of a piece of neutral dielectric Qtotal.

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Most popular questions from this chapter

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When you polarize a neutral dielectric, the charge moves a bit, but the total remains zero. This fact should be reflected in the bound charges σb and ρb· Prove from Eqs. 4.11 and 4.12 that the total bound charge vanishes.

Short Answer

Step by step solution

Write the given data from the question

Determine the formula of total charge of a piece of neutral dielectric Qtotal.

Determine the value of total charge of a piece of neutral dielectric Qtotal.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Physics of Motion

Circular Motion and Gravitation

Geometrical and Physical Optics

Electricity and Magnetism

Solid State Physics

Study anywhere. Anytime. Across all devices.

When you polarize a neutral dielectric, the charge moves a bit, but the total remains zero. This fact should be reflected in the bound charges $σ_{b}$ and $ρ_{b}$ · Prove from Eqs. 4.11 and 4.12 that the total bound charge vanishes.