Two infinitely long parallel wires carry equal and opposite linear charge densities of magnitude λ. For unit wire length, work to increase their separation from a to 2a is [λ²/(xπε₀)]ln y. Find 2(x+y).
Physics · Mixed Chapter
JEE Mains

Question

Two infinitely long parallel wires carry equal and opposite linear charge densities of magnitude λ. For unit wire length, work to increase their separation from a to 2a is [λ²/(xπε₀)]ln y. Find 2(x+y).

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Electric field due to one long charged wire: At separation r, E(r)=λ/(2πε₀r). Step 2 — Attraction per unit length on the opposite wire: F/L = λE(r)=λ²/(2πε₀r). Step 3 — External work required against the attraction: W/L=∫(a→2a) [λ²/(2πε₀r)]dr = [λ²/(2πε₀)]ln2. Step 4 — Match given expression: x=2 and y=2. Step 5 — Requested value: 2(x+y)=2(2+2)=8. Answer: 8.