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STD 12 - 1. Electric charges and fields — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 12 - 1. Electric charges and fields4 Marks
MCQ
The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $\lambda$ are kept parallel to each other. In their resulting electric field, point charges $q$ and $- q$ are kept in equilibrium between them. The point charges are confined to move in the $x$ direction only. If they are given a small displacement about their equilibrium positions, then the correct statement$(s)$ is(are)
  • A
    Both charges execute simple harmonic motion.
  • B
    Both charges will continue moving in the direction of their displacement.
  • ✓
    Charge $+ q$ executes simple harmonic motion while charge $- q$ continues moving in the direction of its displacement.
  • D
    Charge $- q$ executes simple harmonic motion while charge $+ q$ continues moving in the direction of its displacement.
✓

Answer

Correct option: C.
Charge $+ q$ executes simple harmonic motion while charge $- q$ continues moving in the direction of its displacement.
c
In Case $I$ :

$\overrightarrow{ F }=\frac{\lambda q }{2 \pi \varepsilon_0( r + x )} \hat{ i }+\frac{\lambda q }{2 \pi \varepsilon_0( r - x )}(-\hat{ i })$

$=\frac{\lambda q }{\pi \varepsilon_0 I ^2} x (-\hat{ i })$

Hence $+ q$, charge will performs $S H M$ with time period $T =2 \pi \sqrt{\frac{ \pi r ^2 \varepsilon_0 m }{\lambda q }}$

In case II: Resultant force will act along the direction of displacement.

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