Question

If vo be the potential at origin in an electric field e=exi^+eyj^ then the potential at point p(x,y) is

Answer 1

Answer:

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.