Bài tập điện đọng lực học 1

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=>?@A
BCD
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  
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∂ ∂ ∂
+ +
∂ ∂ ∂
ur
r ur
=
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ur
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BCD

ur
@ H H
1. =>?@ 
@



∂
∂
r
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
∂
∂
r
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

∂
∂
r

  
  
  
  
 
∂ ∂ ∂
   
 ÷
 ÷  ÷
∂ ∂ ∂
   
 
∂ ∂ ∂
− − −

∂ ∂ ∂
ur
r ur
@
     
     
     
  
           
     
 ÷  ÷  ÷
 ÷  ÷  ÷
     
∂ ∂ ∂ ∂ ∂ ∂
− + − + −
∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
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r ur
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2. BCD
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ur
@
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 
 
 
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 
        

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 
 ÷  ÷
 ÷
 ÷  ÷
 
   
∂ ∂
∂ ∂
∂ ∂
∂ ∂ ∂
− + − + −
∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
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 
 
     
 
 
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 
 
 
           
∂ ∂
∂ ∂
∂ ∂
− + − + −
∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

@A
 !#$!EI(0!&#/!
 
 
 
r ur
!JK!E)*(-!3F!
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r
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= + +
ur r r r
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    
  
 

 ÷
 
⇒ =
 ÷
 
 ÷
 
r r r
r ur
@
( )
( )
( )
     
              
− − − + −
r r r
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( )
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A
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  
     
  
     

∂ ∂ ∂
 
= − − − + −
 
∂ ∂ ∂
   
∂ ∂ ∂ ∂ ∂ ∂
 
= − + − + − = ⇒
 ÷
 ÷  ÷
∂ ∂ ∂ ∂ ∂ ∂
 
   
r ur
W
S
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 
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 
r ur uur
,!!E)*(-!3F!
  
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#
!!L8!/M7+*)!N0O(-!3P#,!
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⇒
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 ÷
= − − − + −

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 
r r r
r r r
( )
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      
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 
 ÷
 
 
⇒ =

 ÷
 
 
 ÷
 ÷
− − −
 

 
− − −
 


 
= − − − −

 

 
+ − − −

 

r r r
r uuruur
r
r
r
( )
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     
               
     

 
 
= + + + + +
 
 
= + +
= ⇒
r uuruur
W
 !&
!EI(0<!
( )
{ }

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 
 
ur r ur
#
 
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r

!"#$%&'()"
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ur
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= + +
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
 
∂ ∂
−


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 
∂ ∂
 

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
∂ ∂ ∂ ∂ ∂

 
 ÷
⇒ = = − −

 
 ÷
∂ ∂ ∂ ∂ ∂
 

 ÷

 ÷
 
∂ ∂
 
+ −

 
∂ ∂

 


∂ ∂
 
∂ ∂
−
 
∂ ∂ ∂ ∂
 
∂ ∂
 
∂ ∂
= − −
 
∂ ∂ ∂ ∂
 
∂
∂
+ −
∂ ∂
r
r r r
ur r
r
r
r
r
( )
( )
( )
S

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      








∂
 
∂

 
∂ ∂

 

 
∂
   
∂ ∂ ∂ ∂ ∂ ∂
 
= − − − + −

 
 ÷
 ÷  ÷
∂ ∂ ∂ ∂ ∂ ∂ ∂
 
   
 
r r r
TU7
N0R7,!+.!7F<!
   
V V
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     
 
∂ ∂ ∂
= + + ⇒ = = =
 
∂ ∂ ∂
 
( )

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 
 
 
 
 
   

   
   
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 
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 
 
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∂ ∂


−
−


∂ ∂


∂ ∂
 
⇒ − = −
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∂ ∂
 
∂ ∂
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−
−
 
∂ ∂



EW!XYZ!/8!X[Z,!+.!3\]7<!
( )
{ }
A

  
= ⇒
ur
W
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
   
= + +
r r r r
!/8!
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= + +
ur r r r
( )
( )
( )
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  
 

 ÷
 
⇒ = = − − − + −
 ÷
 
 ÷
 
r r r
r ur r r r
_
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( )
( )
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 
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           

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        
 
        
 

 
∂ ∂
− − −

 
 
∂ ∂
 

 ÷

∂ ∂ ∂ ∂ ∂

 
 ÷
 
⇒ = + − − − −

 
 
 ÷
∂ ∂ ∂ ∂ ∂
 


 ÷
 ÷

− − −
 
∂ ∂
 
+ − − −

 
∂ ∂

 

= + + + + +
= +
r
r r r
rur r
r
r r r
r r
( )


 
+ = ⇒
r r
W

 !'$!EI(0<!!!!
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/
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urur
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.
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( )
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   

= + +



= + +

urur

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