An electric dipole consists of charges $\pm 2.0 \times 10^{- 8} C$ separated by a distance of 2.0 × 10^-3m. It is placed near a long line charge of linear charge density 4.0 × 10^-4C/m. as shown in figure, such that the negative charge is at a distance of 2.0 cm from the line charge. Find the force acting on the dipole

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0.6 N towards the line charge

1.5 N away from the line charge

0.1 N away from the line charge

0.9 N towards the line charge

answer is A.

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Detailed Solution

Field due to infinite long line charge at a distance ‘r’ from it $\vec{E} = \frac{λ}{2 π \in_{0} r}$

$\begin{array}{l} F_{-} = \frac{λ q}{2 π ϵ_{0} \times 2 \times 10^{- 2}} and \\ F_{+} = \frac{λ q}{2 π ϵ_{0} \cdot 2.2 \times 10^{- 2}} net force \\ = \frac{λ q}{10^{- 2} \times 2 π ϵ_{0}} [\frac{1}{2} - \frac{1}{2.2}] \\ = \frac{λ q (0.2)}{10^{- 2} \times 2 π ϵ_{0} \times 2.2 \times 2} \end{array}$