Two parallel wires are X₀ apart. A charge moving between them is at distance X₁ from one wire, with X₀/X₁=3. Its path radius is R₁ when equal currents in the wires are in the same direction and R₂ when the currents are opposite. Find R₁/R₂.
Physics · Magnetic effect of current
JEE Advanced 2014

Question

Two parallel wires are X₀ apart. A charge moving between them is at distance X₁ from one wire, with X₀/X₁=3. Its path radius is R₁ when equal currents in the wires are in the same direction and R₂ when the currents are opposite. Find R₁/R₂.

Physics · Magnetic effect of current

JEE Advanced 2014

G1 Physics · Accepted Answer

At the charge, fields of the two wires subtract for currents in the same direction and add for opposite directions. With distances X₁ and X₀−X₁=2X₁, their magnitudes are proportional to 1/X₁ and 1/(2X₁). Thus B(same)∝1/2 and B(opposite)∝3/2. Since r=mv/(qB), R₁/R₂=B(opposite)/B(same)=3.