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 equlibrium positions, then the correct statement(s) is (are) :

Question

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 equlibrium positions, then the correct statement(s) is (are) :

G1 Physics · Accepted Answer

Step 1: Convert the density to charge using dq = ρ dV, dq = λ dl, or dq = σ dA as appropriate. Step 2: Integrate over the stated region and then use Coulomb's law/Gauss's law for the field or flux. Step 3: Apply the given radius/position limits and simplify. Final: C: Charge +q executes simple harmonic motion while charge -q continues moving in the direction of its displacement..