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I really don't know what this is ><

  • Thread starter quietrain
  • Start date
  • #1
654
2

Homework Statement


electrotut2.png


Homework Equations


electrotut.png



The Attempt at a Solution



can anyone enlighten me what the red and blue equations mean? i remembered something about the red eqn meaning unit vector in vector format, or scalar format is it?

and the blue eqn i have totally no idea what my prof is doing >< is he trying to say that del F is a dot product and since they are 0 because i =/= j, that means that cross product is 0???

help appreciated!
 
Last edited:

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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hi quietrain ! :smile:

it's all very simple …

r^/r2 = (r/|r|)/r2 = r/r3

and

∂/∂xi (Fj)

= ∂/∂xi (xj)

= ∂/∂xi (xj/r3)

= {∂/∂xi (xj)}/r3 + {∂/∂xi 1/r3)}xj (product rule)

= 0 + {∂/∂xi 1/r3)}xj :wink:
 
  • #3
654
2
with regards to part b)

for the cross product (del X F) to be 0, are they saying that delyFz - delzFy must be 0 and the other permutations too,

so that delyFz = delzFy

but from the form ∂/∂xi (Fj), it has a minus sign after differientiating, thus for Eijk, if we swop once to Eikj , then the minus sign is gone

so now its minus - plus = 2 minus , not 0?
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
250
hi quietrain! :smile:

(have a del: ∇ and an epsilon: ε :wink:)
for the cross product (del X F) to be 0, are they saying that delyFz - delzFy must be 0 and the other permutations too,

so that delyFz = delzFy
yes :smile:
but from the form ∂/∂xi (Fj), it has a minus sign after differientiating, thus for Eijk, if we swop once to Eikj , then the minus sign is gone

so now its minus - plus = 2 minus , not 0?
ah, you can either write ∇jFk - ∇kFj

or εijkjFk

same thing :wink:
 
  • #5
654
2
hi quietrain! :smile:

(have a del: ∇ and an epsilon: ε :wink:)


yes :smile:


ah, you can either write ∇jFk - ∇kFj

or εijkjFk

same thing :wink:
oh so it becomes minus minus minus which is minus plus = 0
thanks!
 

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