A stream of positively charged particles having q/m=2×10¹¹ C kg⁻¹ and velocity ⃗v₀=3×10⁷ ̂i m s⁻¹ is deflected by an electric field 1.8 ̂j kV m⁻¹. The electric field exists in a region of 10 cm along the x-direction. Due to the electric field, the deflection of the charged particles in the y direct…

Question

A stream of positively charged particles having q/m=2×10¹¹ C kg⁻¹ and velocity ⃗v₀=3×10⁷ ̂i m s⁻¹ is deflected by an electric field 1.8 ̂j kV m⁻¹. The electric field exists in a region of 10 cm along the x-direction. Due to the electric field, the deflection of the charged particles in the y direction is mm.

Accepted Answer

2. The x-motion is unaffected, so the time spent in the field is t=L/(v₀)=(0.10)/(3×10⁷)=3.33×10⁻⁹ s. The transverse acceleration is a=q/mE=2×10¹¹×1.8×10³=3.6×10¹⁴ m s⁻². y=1/2at²=1/2×3.6×10¹⁴×(3.33×10⁻⁹)². t²=1.111×10⁻¹⁷, so y=1/2×4×10⁻³=2×10⁻³ m. The deflection is 2 mm.

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