An electron of mass 0.90×10⁻³⁰ kg moves in a circle of radius 2.0 cm at 3.0×10⁶ m s⁻¹ in a magnetic field. A proton of mass 1.8×10⁻²⁷ kg is to move in a circle of equal radius in the same field. Its speed is 1.5×10ⁿ m s⁻¹. Find n.
Physics · Mixed Chapter
JEE Mains

Question

An electron of mass 0.90×10⁻³⁰ kg moves in a circle of radius 2.0 cm at 3.0×10⁶ m s⁻¹ in a magnetic field. A proton of mass 1.8×10⁻²⁷ kg is to move in a circle of equal radius in the same field. Its speed is 1.5×10ⁿ m s⁻¹. Find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Magnetic force provides centripetal force: For motion perpendicular to a uniform magnetic field, the magnetic force equals the required centripetal force: |q|vB = mv²/r. Step 2 — Rearrange for speed: v = |q|Br/m. An electron and a proton have equal charge magnitude e. Since they move in the SAME field B with the SAME orbit radius r, speed is inversely proportional to mass: vₚ/vₑ = mₑ/mₚ. Step 3 — Substitute masses and electron speed: mₑ = 0.90×10⁻³⁰ kg; mₚ = 1.8×10⁻²⁷ kg; vₑ = 3.0×10⁶…