A wire lies along the parabola y² = 2x and carries current I = 2 A from A to B as shown, with A and B at x = 2 m. It is in uniform field B⃗ = −4k̂ T. The resultant magnetic force is (8x)î N. Find x.
Physics · Mixed Chapter
JEE Mains

Question

A wire lies along the parabola y² = 2x and carries current I = 2 A from A to B as shown, with A and B at x = 2 m. It is in uniform field B⃗ = −4k̂ T. The resultant magnetic force is (8x)î N. Find x.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Magnetic force on a curved current-carrying wire: In a uniform magnetic field, the total force is independent of the wire’s shape: 𝐅 = I(𝐫 at B − 𝐫 at A) × 𝐁. Step 2 — Endpoints from the parabola: y² = 2x; at x = 2 m, y = ±2 m. The displacement from A to B shown in the figure is −4ĵ m. Step 3 — Cross product and magnitude: I = 2 A, 𝐁 = −4k̂ T. 𝐅 = 2(−4ĵ) × (−4k̂) = 32î N. Step 4 — Requested integer: 32 = 8x ⇒ x = 4. Answer: 4.