A stream of a positively charged particles having and velocity is deflected by an electric field . The electric field exists in a region of 10 cm along direction. Due to the electric field, the deflection of the charge particles in the direction is ______ mm.
Show answer and solution
Answer: 2
Solution
The electric field provides acceleration in the y-direction: a = (q/m)·E = 2×10¹¹ × 1.8×10³ = 3.6×10¹⁴ m/s².
Time spent in the field region: t = L/v₀ = 0.1/(3×10⁷) = (1/3)×10⁻⁸ s.
Deflection y = (1/2)·a·t² = (1/2) × 3.6×10¹⁴ × (1/9)×10⁻¹⁶ = (1/2) × 4×10⁻² × 10⁻¹ = 2×10⁻³ m = 2 mm.
Time spent in the field region: t = L/v₀ = 0.1/(3×10⁷) = (1/3)×10⁻⁸ s.
Deflection y = (1/2)·a·t² = (1/2) × 3.6×10¹⁴ × (1/9)×10⁻¹⁶ = (1/2) × 4×10⁻² × 10⁻¹ = 2×10⁻³ m = 2 mm.
[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]