Q19P Calculate鈭嚸桬directly from Eq.... [FREE SOLUTION]

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Introduction to Electrodynamics

David J. Griffiths

Physics

4th edition Edition 路 613 pages

ISBN: 9780321856562

Chapter 2: Q19P (page 78)

Calculate $鈭� 脳 E$ directly from Eq. 2.8, by the method of Sect. 2.2.2. Refer to Prob. 1.63 if you get stuck.

Short Answer

Expert verified

The required value is $鈭� 脳 E (r) = 0$

Step by step solution

Determine the expression for the electric field in the two sphere.

Write the formula for the electric field of the volume charge.

$E (r) = \frac{1}{4 {蟺蔚}_{0}} 鈭� \frac{蚁 (r^{'})}{r^{2}} \overset{炉}{r} d_{T'}$

Write the curl of the above function as,

$鈭� 脳 E (r) = \frac{1}{4 {蟺蔚}_{0}} 鈭� 鈭� 脳 \frac{(\overset{炉}{r})}{r^{2}} r' {蚁d}_{T'}$ 鈥�.. (1)

Here, $蔚_{0}$ is the permittivity of the free space and $蚁$ is the charge density.

Determine the value of ∆×(r¯)r2.

Solve for $鈭� 脳 \frac{(\overset{炉}{r})}{r^{2}}$ as,

localid="1655897481663" $鈭� 脳 \frac{(\overset{炉}{r})}{r^{2}} = (\frac{1}{r^{2}} \frac{鈭�}{鈭� r} \overset{炉}{r} + \frac{1}{r \sin 胃} \frac{鈭�}{鈭� 蠒} \overset{炉}{蠒}) 脳 (r^{n} 蠒) = |\begin{matrix} \overset{炉}{r} & \hat{胃} & \hat{蠒} \\ \frac{1}{r^{2}} \frac{鈭�}{鈭� r} & \frac{1}{r \sin 胃} \frac{鈭�}{鈭� 胃} & \frac{1}{r \sin 胃} \frac{鈭�}{鈭� 蠒} \\ r^{2} & 0 & 0 \end{matrix}| = \hat{r} (0 - 0) - \hat{胃} (0 - \frac{1}{r \sin 胃} \frac{鈭�}{鈭� 蠒} r^{2}) + \hat{蠒} (0 - \frac{1}{r \sin 胃} \frac{鈭�}{鈭� 蠒} r^{2}) = 0$

Substitute 0 for $鈭� 脳 \frac{(\hat{r})}{r^{2}}$ in the equation $鈭� 脳 E (r) = \frac{1}{4 p 蔚_{0}} 鈭� 鈭� 脳 \frac{(\hat{r})}{r^{2}} r^{'} p d 蟿$ .

$鈭� 脳 E (r) = \frac{1}{4 p 蔚_{0}} (0) = 0$

Therefore, the required value is $鈭� 脳 E (r) = 0 .$

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91影视

Calculate $鈭� 脳 E$ directly from Eq. 2.8, by the method of Sect. 2.2.2. Refer to Prob. 1.63 if you get stuck.

Short Answer

Step by step solution

Determine the expression for the electric field in the two sphere.

Determine the value of ∆×(r¯)r2.

One App. One Place for Learning.

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91影视

Calculate鈭�脳Edirectly from Eq. 2.8, by the method of Sect. 2.2.2. Refer to Prob. 1.63 if you get stuck.

Short Answer

Step by step solution

Determine the expression for the electric field in the two sphere.

Determine the value of ∆×(r¯)r2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Measurements

Turning Points in Physics

Magnetism

Fundamentals of Physics

Translational Dynamics

Study anywhere. Anytime. Across all devices.

Calculate $鈭� 脳 E$ directly from Eq. 2.8, by the method of Sect. 2.2.2. Refer to Prob. 1.63 if you get stuck.