A, B, C, D, P, and Q are points in a uniform electric field. The potentials at these points are `V(A) = 2 V. V(P) = V( B) = V(D) = 5 V`, and `V(C) = 8 V`. Find the electric field at P.
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Explanation

Method I : The component of electric field in x - direction is
`E_x = -(Delta V)/(Delta x) = (-[V_D - V_A])/((0.2)) = (-[5 - 2])/(0.2) = - 15 Vm^-1`
Similarly,
`E_y = -(Delta V_y)/(Delta y)= (-[V_B - V_A])/(0.2) = (-[5 -2])/(0.2)= -15 Vm^-1`
Hence, electric field `vec E = E_x hat i + E_y hat j = - 15 hat i - 15 hat j (V m^-1)`
Method II : The points (B, p, and D) have same potential , hence, these points will lie on same equipotential surface. The separation between two rquipotentials is
`A P = 0.1 xx sqrt (2) m`
`|E| ((5 -2))/(0.1 sqrt(2)) = 15 sqrt(2) Vm^-1`
`E_(PA) = 15 sqrt (2) Vm^-1`
Here
`vec E = 15 sqrt(2) cos 45^(@) (- hat i) + 15 sqrt(2) sin 45^(@) (- hat j)`
=`- 15 hat i - 15 hat j Vm^-1`.
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