A particle of mass 10−3 kg and charge 1.0 C, is initially at rest. At time t=0, the particle comes under the influence an electric field →E(t)=E0sin(ωt) ^i where E0=1.0NC−1 and ω=103 rad s−1. Consider the effect of only the electrical force on the particle. Then the maximum speed, in ms−1, attained by the particle at subsequent times is __________.
n=10−3kg,q=1C,t=0
E = E0sinωt
Force on particle will be
F=qE=qE0sinωt
At vmax,a,F=0
qE0sinωt=0
F=qE0sinωt
dvdt=qE0msinωt
∫v0dv=∫π/ω0qE0msinωtdt
v−0=qE0mω[−cosωt]πω0
v−0=qE0mω[(−cosπ)–(cos0)]
v=1×110−3103×2=2m/s