Question

An electric field is given by `vec(E)=(yhat(i)+xhat(j))N/C`. Find the work done (in J) in moving a `1 C` charge from `vec(r)_(A)=(2hat(i)+2hat(j))` m to `vec(r)_(B)=(4hat(i)+hat(j))m`.

Answer 1

`A=(2, 2)` and `B=(4, 1), W_(A to B)=q(V_(B)-V_(A))=q underset(A)overset(B)(int)dV=- underset(A)overset(B)(int)qvec(E).dvec(r)`
`=qunderset(A)overset(B)(int)("yhat(i)+xhat(j)).(dxhat(i)+dyhat(j))=qunderset(A)overset(B)int(ydx+xdy)=-q underset("(2, 2)")overset("(4, 1)")(int)d(xy)=-q[xy]_("(2,2)")^("(4, 1)")=-q[4-4]=0`