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An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 × 10⁻⁶ C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm respectively from its origin. If total force of 4 N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

1. 815.1 nC
2. 8.8 μC
3. 0.485 mC
4. 4.44 μC

Correct answer: 4.44 μC

Solution

Line-charge field E = lambda/(2*pi*eps0*r) = 2k*lambda/r. Net force on dipole = q*2k*lambda*(1/r1 - 1/r2) with r1=0.010 m, r2=0.012 m: 2k*lambda = 2*9e9*3e-6 = 5.4e4, and (1/0.010 - 1/0.012) = 16.67 /m, so F = q*5.4e4*16.67 = q*9.0e5. Setting F = 4 N gives q = 4/9.0e5 = 4.44 microC.

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