87. Electric Field from Electric Potential in Two Dimensions

# 87. Electric Field from Electric Potential in Two...

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Electric Potential from Electric Field in Two Dimensions Given is the electric field: ~ E = - (2 ax + by 3 ) ˆ i - 3 bxy 2 ˆ j with a = 1 V/m 2 , b = 1 V/m 4 . Find the electric potential V ( x, y ) via integral along a specific path: Red path (0 , 0) (0 , y ) ( x, y ) : V ( x, y ) = - Z y 0 E y (0 , y ) dy - Z x 0 E x ( x, y ) dx = 0 + Z x 0 (2 ax + by 3 ) dx = ax 2 + bxy
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Unformatted text preview: Blue path (0 , 0) → ( x, 0) → ( x, y ) : V ( x, y ) =-Z x E x ( x, 0) dx-Z y E y ( x, y ) dy = Z x (2 ax ) dx + Z y (3 bxy 2 ) dy = ax 2 + bxy 3 x (x,0) (x,y) (0,y) (0,0) y tsl87 – p.1/1...
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