An electron enters the region between the plates of a parallel-plate capacitor with horizontal speed vₓ = 10⁶ m/s. The plate length is ℓ = 10 cm and the electric field magnitude is E = 9.1 N/C.
Given electron mass m = 9.1×10⁻³¹ kg, find the magnitude of vᵧ when the electron leaves the plates.

Question

An electron enters the region between the plates of a parallel-plate capacitor with horizontal speed vₓ = 10⁶ m/s. The plate length is ℓ = 10 cm and the electric field magnitude is E = 9.1 N/C.

Given electron mass m = 9.1×10⁻³¹ kg, find the magnitude of vᵧ when the electron leaves the plates.

G1 Physics · Accepted Answer

Time inside the field: t = ℓ/vₓ. Acceleration magnitude: a = eE/m. Therefore, vᵧ = at = (eE/m)(ℓ/vₓ). Substituting, vᵧ = [(1.6×10⁻¹⁹)(9.1)(10⁻¹)]/ [(9.1×10⁻³¹)(10⁶)] = 1.6×10⁵ m/s.