Chapter 1. calc_tutorial_16_1_029

1.1 Problem Statement

{2,3,4,5,6,7,8,9}

Let φ = $a ln r, where . Express ∇φ in terms of the unit radial vector er in R2.

1.2 Step 1

Question Sequence

Question 1.1

Use the chain rule for gradients to evaluate ∇φ.

∇φ = ∇($a ln r) = nc1ItEz0kR4=(∇r / r)

Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Evaluate ∇r, where .

∇r = <(∂r / ∂x), (∂r / ∂y)> =

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
Correct.
Incorrect.

1.4 Step 3

Question Sequence

Question 1.3

Express ∇φ in terms of the unit radial vector er in R2.

∇φ = $a(∇r / r) = ($a / r)<x / r, y / r> = nc1ItEz0kR4=(er / r)

Correct.
Incorrect.