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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 4 N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

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$815.1 n C$

$8.8 μ C$

$0.485 m C$

$4.44 μ C$

answer is D.

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Detailed Solution

$r = 10 m m, x = 2,$

$| {\vec{F}}_{q} | = \frac{2 k λ}{r} . q$

$| {\vec{F}}_{- q} | = \frac{2 k λ}{r + x} . q \Rightarrow | {\vec{F}}_{n e t} | = \frac{2 k λ q}{r} - \frac{2 k λ q}{r + x}$

$| {\vec{F}}_{n e t} | = \frac{2 k λ q \cdot x}{r (r + x)}$

$4 = \frac{2 \times 9 \times 10^{9} \times 3 \times 10^{- 6} \times q \times 2 mm}{10 mm .12 mm} \Rightarrow q = 4.44 μ C$

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