Discussion Forum

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 of an electric field E (t)= E₀  sin ωt  $\hat{i}$, where E₀ = 1.0N C^-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..........

Answer:

Explanation:

               $a=\frac{F}{m}=\frac{qE}{m}=10^{3}\sin(10^{3}t)$

                $\frac{\text{d}v}{\text{d}t}=10^{3}\sin(10^{3}t)$

   $\Rightarrow$      $\int_{0}^{v}dv =\int_{0}^{t} 10^{3}\sin(10^{3}t) dt$

$\therefore$     $v= \frac{10^{3}}{10^{3}}[1-\cos (10^{3}t)]$

    Velocity  will be maximum when $\cos(10^{3}t)=-1$

                        v_max = 2 m/s