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    Question

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

    βˆ’3, 1). Find the electric potential at point B(4, βˆ’1, 0) in volts. (Use 1/(4 Ο€ Ξ΅0) = 9 Γ— 109 Nm2/C2
    A 10.89 Γ— 109V Correct Answer Incorrect Answer
    B 13.54 Γ— 109V Correct Answer Incorrect Answer
    C 5.31 Γ— 109V Correct Answer Incorrect Answer
    D 4.67 Γ— 109V Correct Answer Incorrect Answer

    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, βˆ’3, 1) and the point B(4, βˆ’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+3jβˆ’4k. Now, we calculate the dot product p β‹… r: p β‹… r=(2)(2)+(3)(2)+(βˆ’4)(βˆ’1)=4+6+4=14 The electric potential at point B is:

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