A dipole with moment p = 2i + 3j - 4k is placed at A(2,

Solution

The electric potential V at a point due to an electric dipole with dipole moment p is given by: where r is the vector from the location of the dipole to the point at which the potential is being calculated, and r= ∣ r ∣ is the magnitude of this vector. Given the position of the dipole at A(2, −3, 1) and the point B(4, −1, 0) where the potential is to be found, the vector r is given by: r = rB – rA = (4-2)i + (-1-(-3))j+(0-1)k = 2i+2j-k The magnitude of r is: The dipole moment is given as p=2i+3j−4k. Now, we calculate the dot product p ⋅ r: p ⋅ r=(2)(2)+(3)(2)+(−4)(−1)=4+6+4=14 The electric potential at point B is: