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CBSE Class 12-science Answered

What is the relation between electric field and potential difference?
Asked by yashrajgharte24.12dgatl | 19 Jul, 2021, 03:41: PM
Expert Answer
Relation between Electric field begin mathsize 14px style E with rightwards arrow on top end style and Gradient of potential begin mathsize 14px style nabla end styleV is given as
begin mathsize 14px style E with rightwards arrow on top end style = - begin mathsize 14px style nabla end styleV
In Cartesian coordinate system , above relation can be written as
 
begin mathsize 14px style open parentheses E subscript x space i with hat on top space plus space E subscript y space j with hat on top space plus E subscript z k with overbrace on top space close parentheses space equals space minus space open parentheses fraction numerator partial differential V over denominator partial differential x end fraction space space i with hat on top space plus fraction numerator partial differential V over denominator partial differential y end fraction space space j with hat on top space plus space fraction numerator partial differential V over denominator partial differential z end fraction space space k with hat on top space space space space close parentheses end style
Where Ex , Ey and Ez are electric field components  and begin mathsize 14px style i with hat on top space comma space j with hat on top space a n d space k with hat on top end style are unit vectors
along x, y and z-axis direction
Answered by Thiyagarajan K | 19 Jul, 2021, 05:00: PM
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