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An electric dipole lies on the x-axis near a long line charge of linear density 3.0 * 10⁻⁶ C/m placed along the z-axis. The dipole's positive and negative charges are at 10 mm and 12 mm from the origin respectively. If the net force on the dipole is 4 N, find the magnitude of each charge of the dipole.

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

Correct answer: 4.44 microC

Solution

Each dipole charge experiences the line-charge field E = lambda/(2*pi*eps0*r). The +q at 10 mm is pushed outward, the -q at 12 mm pulled inward, so the net force is q*lambda/(2*pi*eps0)*(1/0.010 - 1/0.012) = 4 N. Solving, q = 4 / [ (lambda/(2*pi*eps0)) * (1/0.010 - 1/0.012) ] = 4.44 microC.

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