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A dipole with dipole moment p = 2i - 3j + 4k is located at point A(2, -3, 1). The electric potential it produces at point B(4, -1, 0) is written as (ab) x 10⁹ volt, where 'a' encodes the sign (a = 0 if the answer is negative, a = 1 if positive) and 'b' is the rounded numerical magnitude. Find the value of (a+b)². All quantities are in SI units.
- 0
- 1
- 4
- 9
Correct answer: 4
Solution
Displacement r = B - A = (2, 2, -1), |r| = sqrt(4+4+1) = 3, r³ = 27. p. r = 2*2 + (-3)*2 + 4*(-1) = 4 - 6 - 4 = -6. V = 9e9 * (-6)/27 = -2 x 10⁹ V. The result is negative so a = 0, and its magnitude is 2 so b = 2. Therefore (a+b)² = (0+2)² = 4.
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