Find the potential difference `V_(AB)` between `A (0,0,0) and B (1 m , 1 m,1 m)` in an electric field :
(i) `vec E = (y hat i + x hat j) Vm^-1`
(ii) `vec E = (3 x^2 y hat i + x^3 hat j) Vm^-1`.

Explanation

To find the potential difference \( V_{AB} \) between points \( A(0,0,0) \) and \( B(1,1,1) \) in the given electric fields, we will use the formula for the potential difference in a non-uniform electric field:

\[ V_{AB} = -\int_A^B \vec{E} \cdot d\vec{r} \]

where \( \vec{E} \) is the electric field and \( d\vec{r} \) is the differential displacement vector.

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