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Find the potential difference V(AB) betw...

Find the potential difference `V_(AB)` between `A(2m, 1m, 0)` and `B(0, 2m, 4m)` in an electric field,
`E=(xhati-2yhatj+zhatk)V/m`

Text Solution

Verified by Experts

`dV = vec(E ).dvec(r )`
`underset(B)overset(A)int dV = - underset((0,2,4))overset((2,1,0))int (x vec(i) - 2y vec(j) + z vec(k)).(dx vec(i) + dy vec(j) + dz vec(k))`
`:. V_(A) - V_(B) = -underset((0,2,4))overset((2,1,0))int (xdx-2ydy + zdz)`
`V_(1B) = -[(x^(2))/(2) - y^(2) + (z^(2))/(2)]_((0,2,4))^((2, 1, 0)) = 3` volt
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