1) How can I know if the field is gradient? 2) How can I know if the fiels is conservative ? 3) How can I find the function potential of vector field ?
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Originally Posted by Apprentice123 1) How can I know if the field is gradient? 2) How can I know if the fiels is conservative ? 3) How can I find the function potential of vector field ? 1) If for some 2) If 3) Set and solve for .
if I have what will be: and
Originally Posted by Apprentice123 if I have what will be: and Since you only have a two dimensional vector field, say then this would be conservative if and if and then and which are identical. So the vector field is conservative and an exists such that and which gives
for the field is conservative ? field conservative = field gradient ? If and why ???
Originally Posted by Apprentice123 for the field is conservative ? field conservative = field gradient ? If and why ??? First since the vector field is conservative you know an exists, i.e. exists such that If then integrating wrt to gives . Now subs. into which shows that which gives which gives , thus our
Thank you I understand. And the statements are correct? for that the field is conservative i need have => and field conservative = field gradient ?
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