Chapter 10: Q7P (page 513)

Write in terms of $δ' s$ as in $(5.8)$ and $(5.9)$ :
(a) $ε_{i j k} ε_{p j q}$ (b) $ε_{a b c} ε_{p q c}$

Short Answer

Expert verified

The terms of part $(a)$ and $(b)$ are $δ_{q k} δ_{p i} - δ_{q i} δ_{p k}$ and $δ_{a p} δ_{b q} - δ_{a q} δ_{b p}$

Step by step solution

Given Information

The equation, i.e., $ϵ_{i j k} ϵ_{i m n} = δ_{j m} δ_{k n} - δ_{j n} δ_{k m}$ .

The equation, i.e., $ϵ_{a b c} ϵ_{p q b} = ϵ_{b c a} ϵ_{b p q} = δ_{c p} δ_{a q} - δ_{c q} δ_{a p}$ .

Definition ofIsotropic tensor.

The term “isotropic tensor” refers to a tensor whose components remain intact when the coordinate system is rotated arbitrarily.

Solve for part (a)

Use the equation. $(5.8)$

$\begin{matrix} ϵ_{i j k} ϵ_{p j q} = ϵ_{j k i} ϵ_{j q p} \\ = δ_{q k} δ_{p i} - δ_{q i} δ_{p k} \end{matrix}$

Hence, the terms $δ' s$ are $δ_{q k} δ_{p i} - δ_{q i} δ_{p k}$

Solve for part (b)

Use the equation. $(5.9)$

$\begin{matrix} ϵ_{a b c} ϵ_{p q c} = ϵ_{c a b} ϵ_{c p q} \\ = δ_{a p} δ_{b q} - δ_{a q} δ_{b p} \end{matrix}$

Hence,the terms $δ' s$ are. $δ_{a p} δ_{b q} - δ_{a q} δ_{b p}$

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Write in terms of $δ' s$ as in $(5.8)$ and $(5.9)$ :
(a) $ε_{i j k} ε_{p j q}$ (b) $ε_{a b c} ε_{p q c}$

Short Answer

Step by step solution

Given Information

Definition ofIsotropic tensor.

Solve for part (a)

Solve for part (b)

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Write in terms ofδ'sas in(5.8)and(5.9):(a)εijkεpjq(b)εabcεpqc

Short Answer

Step by step solution

Given Information

Definition ofIsotropic tensor.

Solve for part (a)

Solve for part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Scientific Method Physics

Measurements

Linear Momentum

Turning Points in Physics

Work Energy and Power

Study anywhere. Anytime. Across all devices.

Write in terms of $δ' s$ as in $(5.8)$ and $(5.9)$ :
(a) $ε_{i j k} ε_{p j q}$ (b) $ε_{a b c} ε_{p q c}$