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Vyse007
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I was just reviewing some of my concepts of electrostatics, and I am really confused in some things.
1) Why does E equal the negative gradient of V? I understand the definition of the gradient, but in my mind I am just unable to grasp as to why it should be negative only.
2) Why is the work done in moving a charge through an electric field given by W= -Q[tex]\int^{a}_{b}[/tex]E.dl , where a is the initial position and b is the final position? I mean, how did the negative sign end up there? From what I read about the definition of work, its simply the dot product of the force and the displacement. Then why is it negative? Also, isn't work done against the field positive?
I am just unable to visualize these questions in my head. Any help would be really appreciated.
Thanks in advance.
1) Why does E equal the negative gradient of V? I understand the definition of the gradient, but in my mind I am just unable to grasp as to why it should be negative only.
2) Why is the work done in moving a charge through an electric field given by W= -Q[tex]\int^{a}_{b}[/tex]E.dl , where a is the initial position and b is the final position? I mean, how did the negative sign end up there? From what I read about the definition of work, its simply the dot product of the force and the displacement. Then why is it negative? Also, isn't work done against the field positive?
I am just unable to visualize these questions in my head. Any help would be really appreciated.
Thanks in advance.
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