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An electric field is given by E=(y hat(i...

An electric field is given by `E=(y hat(i)+ xhat(k))N//C`. Work done in moving a 1C charge from `r_(A)=(2hat(i)+2hat(j))m` to `r_(B)=(4hat(i)+hat(j))m` is

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`W=q int_(vecr_(A))^(vecr_(B)) vec(E )* dvec(r )=1xxint_(2,2)^(4,1) (E_(x)dx+E_(y)dy)`
`=1xxint_(2,2)^(4,1)(y dx+x dy)= int_(2,2)^(4,1)d(xy)`
`[xy]_(2,2)^(4,1)=4xx1-2xx2=0`.
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