A particle, of mass $$10$$−$$3kg$$ and charge $$1.0C$$, is initially at rest. At time $$t=0$$, the particle comes under the influence of an electric field $$Et=E0sin$$ωt i⌢, where $$E0=1.0N/C$$ and ω$$=103rad/s$$. Consider the effect of only the electrical force on the particle. Then the maximum speed, in $$m/s$$ , attained by the particle at subsequent times is .

Question

A particle, of mass $$10$$−$$3kg$$ and charge $$1.0C$$, is initially at rest. At time  $$t=0$$, the particle comes under the influence of an electric field  $$Et=E0sin$$ωt i⌢, where $$E0=1.0N/C$$  and  ω$$=103rad/s$$. Consider the effect of only the electrical force on the particle. Then the maximum speed, in $$m/s$$ , attained by the particle at subsequent times is   .

Infinity Learn · Accepted Answer

$$m=10$$−$$3kg$$ $$q=1C$$ $$t=0$$ $$E=E0sin$$⁡ωt Force on particle will be  $$F=qE=qE0sin$$⁡ωt At mean position, speed id Vmax, and, $$F=0$$⇒$$qE0sin$$⁡ω$$t=0$$⇒ω$$t=$$π⇒$$t=$$πω Now, $$F=qE0sin$$⁡ωt⇒$$dVdt=qE0msin$$⁡ωt⇒∫$$0v$$ $$dv=$$∫$$0$$π$$/$$ω $$qE0msin$$⁡ωtdt⇒V−$$0=qE0m$$ω[−$$cos$$⁡ωt]$$0$$π$$/$$ω⇒V−$$0=qE0m$$ω[$$($$−$$cos$$⁡π$$)$$−$$($$−$$cos$$⁡$$0)$$]⇒$$V=1$$×$$110$$−$$3103$$×$$2=2m/s$$

Electric field

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