An electric dipole is placed on x-axis in proximity to a line charge… | JEE Main 2021 (22 Jul, Shift 2)

Q56JEE Main 2021 · 22 JUL · SHIFT 2Difficult

Electric Dipole

An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 $\times$ 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 from the origin respectively. If total force of 4N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

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Answer: (d)

Line charge field: $E = \frac{2k\lambda}{r}$ , with $2k\lambda = 2\times9\times10^9\times3\times10^{-6} = 5.4\times10^4$ .
Net force: $F = q\cdot2k\lambda\left(\frac{1}{0.010} - \frac{1}{0.012}\right) = q\times5.4\times10^4\times16.67 = q\times9\times10^5$
$4 = q\times9\times10^5 \Rightarrow q = 4.44\times10^{-6}$ C
So the answer is (d) 4.44 $\mu$ C.

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