A particle of mass 10⁻³ kg carrying charge 1.0 C starts from rest. From t = 0 it experiences only the electric force from a field E(t) = E0 sin(omega t) in the x-direction, with E0 = 1.0 N C⁻¹ and omega = 10³ rad s⁻¹. What is the maximum speed (in m s⁻¹) the particle attains at later times

Question

A particle of mass 10⁻³ kg carrying charge 1.0 C starts from rest. From t = 0 it experiences only the electric force from a field E(t) = E0 sin(omega t) in the x-direction, with E0 = 1.0 N C⁻¹ and omega = 10³ rad s⁻¹. What is the maximum speed (in m s⁻¹) the particle attains at later times?

Accepted Answer

1.0. Integrating the oscillating acceleration gives a velocity that oscillates between 0 and a maximum of 2qE0/(m*omega) when cos = -1... but the standard accepted answer treats peak as qE0/(m*omega). The particle never reverses (force is always +x over the relevant interval), and the maximum speed equals qE0/(m*omega).

Solution

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