JEE Advanced · Physics · 17. Electrostatics

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $λ$ 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 statements(s) is (are)

A Both charges execute simple harmonic motion
B Both charges will continue moving in the direction of their displacement
C Charges $+ q$ executes simple harmonic motion while charges $- q$ continues moving in the direction of its displacement
D Charge $- q$ executes simple harmonic motion while charges $+ q$ continues moving in the direction of its displacement

Verified Solution

Answer & Solution

Correct Answer

(C) Charges $+ q$ executes simple harmonic motion while charges $- q$ continues moving in the direction of its displacement

Step-by-step Solution

Detailed explanation

In first case if q is shifted towards one of the wires, its repulsive force will increase which will bring the charge back. In second case, in same type of displacement attractive force due to wire increases which will make it move further towards wire.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

	List I		List II
$(a)$	String $- 1 (μ)$	$(p)$	$1$
$(b)$	String $- 2 (2 μ)$	$(q)$	$\frac{1}{2}$
$(c)$	String $- 3 (3 μ)$	$(r)$	$\frac{1}{\sqrt{2}}$
$(d)$	String $- 4 (4 μ)$	$(s)$	$\frac{1}{\sqrt{3}}$
		$(t)$	$\frac{3}{16}$
		$(u)$	$\frac{1}{16}$

Explore more questions on app

From JEE Advanced

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

	List-I		List-II
(I)	$10^{- 3} kg$ of water $100 ° C$ is converted to steam at the same temperature, at a pressure of $10^{5} Pa$ . The volume of the system changes from $10^{- 6} m^{3}$ to $10^{- 3} m^{3}$ in the process. Latent heat of water $= 2250 kJ {kg}^{- 1}$	(P)	$2 kJ$
(II)	$0.2$ moles of a rigid diatomic ideal gas with volume $V$ at temperature $500 K$ undergoes an isobaric expansion to volume $3 V$ . Assume $8.0 J {mol}^{- 1} K^{- 1}$	(Q)	$7 kJ$
(III)	One mole of a monoatomic ideal gas is compressed adiabatically from volume $V = \frac{1}{3} m^{3}$ and pressure $2 kPa$ to volume $\frac{V}{8}$ .	(R)	$4 kJ$
(IV)	Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 kJ$ of heat and undergoes isobaric expansion.	(S)	$5 kJ$
		(T)	$3 kJ$

Which one of the following options is correct?

JEE Advanced 2022 Medium

Columns 1, 2 and 3 contain starting materials, reaction conditions and type of reactions respectively.

Column 1	Column 2	Column 3
(I) Toulene	(i) $NaOH$ $ /Br _2$	(P) Condensation
(II) Acetophenone	(ii) $B r_2 / h v$	(Q) Carboxylation
(III) Benzaldehyde	(iii) $\left( CH _3 CO \right)_2$ $O / CH _3$ $COOK$	(R) Substitution
(IV) Phenol	(iv) $NaOH$ $/CO _2$	(S) Haloform

The only CORRECT combination that gives two different carboxylic acids is

JEE Advanced 2017 Medium

Explore more questions on app

	List-I		List-II
\((P)\)		\((1)\)
\((Q)\)		\((2)\)
\((R)\)		\((3)\)
\((S)\)		\((4)\)
		\((5)\)