Let v0 be the potential at the origin in an electric field e =exi^+eyj^. The potential at the point (x,y) is:
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Let the electric field vector E→=Exi^+Eyj^+Ezk^
VA−VB=−∫ABE→.dr
V(1,0,0)−V(0,0,0)=−∫(1,0,0)(0,0,0)Ex=[−Exx](1,0,0)(0,0,0)
8−10=−Ex
Ex=2
Similarly V(0,1,0)−V(0,0,0)=−∫(0,1,0)(0,0,0)Eydy
−2=−Ey×1
Similarly Ez=2
Thus
E→=2i^+2j^+2k^
Now
V(1,1,1)−V(0,0,0)=−∫(1,1,1)(0,0,0)(2i^+2j^+2k^).(dxi^+dyj^+dzk^)
=−∫(1,1.1)(0,0,0)(2dx+2dy+2dz)
=−(2×1+2×1+2×1)
V(1,1,1)−10=−6
V(1,1,1)=4V.
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