A uniform electric field of magnitude `325 Vm^-1` is directed in the negative y - direction in (fig. 3.12). Theb coordinates of point A are `(-0.2 m , -0.3 m)` and those of point B are `(0.4 m, 0.5 m)`. Calculate the potential difference `V_B - V_A` along the path shown in the figure.
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Explanation

We can define the potential difference between the points A and B.
`V_B - V_A = - undersetAoversetB(int) vec E. vec d s`
= `- undersetAoversetB(int) (E_x hat i + E _y hat j + E _z hat k).(d x hat i + d y hat j + d z hat k)`
= `- [ E_x underset(x_ A)overset(x_B)(int) dx + E_y underset(y_ A)overset(y_B)(int) d y + E_z underset(z_ A)overset(z_B)(int)d z]`
=`-[E_x (x_B - x_A) + E_y (y_B - y_A) + E_z(z_B - z_A)]`
=`-[( -325)^5 {(0.5) - (-0.3)^3} ] = 325 xx 0.8 = 260 V`
`V_B - V_A = + 260 V`.