calc_tutorial_16_1_029

 
Problem Statement

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

Let φ = 7 ln r, where . Express ∇φ in terms of the unit radial vector er in R2.

 
Step 1

Question Sequence

Question 1

Use the chain rule for gradients to evaluate ∇φ.

∇φ = ∇(7 ln r) = (∇r / r)

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

Evaluate ∇r, where .

∇r = <(∂r / ∂x), (∂r / ∂y)> =

A.
B.
C.
D.
Correct.
Incorrect.

 
Step 3

Question Sequence

Question 3

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

∇φ = 7(∇r / r) = (7 / r)<x / r, y / r> = (er / r)

Correct.
Incorrect.