A particle of mass 5 g and charge 12 μC enters a uniform magnetic field B = 100 T at point A of a rectangular region 8 m × 6 m, moving along AB. It leaves at corner C. Find its speed on leaving (m s⁻¹). [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A particle of mass 5 g and charge 12 μC enters a uniform magnetic field B = 100 T at point A of a rectangular region 8 m × 6 m, moving along AB. It leaves at corner C. Find its speed on leaving (m s⁻¹). [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Magnetic force supplies centripetal force: |q|vB = mv²/r, or v = |q|Br/m. Step 2 — A trajectory starting horizontally at A and passing through C (8 m across and 6 m up) has circle centre at (0,r); hence 8² + (6−r)² = r². Step 3 — Solve: r = 100/12 = 25/3 m. Step 4 — v = (12 × 10⁻⁶ × 100 × 25/3)/(5 × 10⁻³) = 2 m s⁻¹.