- #1

rsammas

- 3

- 0

## Homework Statement

Show that:

∇x(∇x

__B__) = (

__B__∇)

__B__- ∇ (1/2B

^{2})

## Homework Equations

__r__= (x,y,z) = x

_{i}

__e__

_{i}

∂x

_{i}/∂x

_{j}= δ

_{ij}

r

^{2}= x

_{k}x

_{k}

δ

_{ij}= 1 if i=j, 0 otherwise (kronecker delta)

ε

_{ijk}is the alternating stress tensor and summ

^{n}conv

^{n}is assumed.

## The Attempt at a Solution

On the LHS I simplified to get:

ε

_{ijk}∂

^{2}/∂x

_{j}∂x

_{k}

but was unsure what to do next because the RHS contains only first order derivatives

On the RHS I was able to get to:

(

__B__∇)

__B__- ∇ (1/2B

^{2}) =

__B__(∂B

_{i}/∂i)-

__B__

=

__B__(∂B

_{i}/∂i-1)

I feel like I'm just not seeing some simple trick, or there is a rule that I don't remember/haven't learned. This is for my Classical Mechanics class BTW.