Derivative of the integral...

[emforum2022]

Hello,
In the Science paper I found the expression for magnetic Force (F) calculated from energy (W'), as it shown in the picture bellow:

Please could you help me with explanation, how the final expression for force F is derived after substituting W' in the first expression for force F. Instantaneous is mentioned in figure? Why lambda was used as a constant for integration (it is also a function of a variable i)? Just the variable i is added after integrating (di) and lambda is written like a constant?
Thanks and best regards
Ernest

 

[Deleted member 4993]

Hello,
In the Science paper I found the expression for magnetic Force (F) calculated from energy (W'), as it shown in the picture bellow:
View attachment 32818
Please could you help me with explanation, how the final expression for force F is derived after substituting W' in the first expression for force F. Instantaneous is mentioned in figure? Why lambda was used as a constant for integration (it is also a function of a variable i)? Just the variable i is added after integrating (di) and lambda is written like a constant?
Thanks and best regards
Ernest

Have you tried to apply Liebniz' rule to calculate the derivative?

Please show us what you have tried and exactly where you are stuck.

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