Oscillating Charge - Max Kinetic Energy

Electricity and Magnetism Level 4

There is a massive charged particle ( m = 4 k g , q = 2 C ) (m = 4\,kg, q = 2C) at rest at the origin ( x = 0 m ) (x = 0m) at time t = 0 t = 0 . The particle is influenced by an electric field oriented purely in the x x direction. It's value is given by:

E x = 3 sin ⁡ ( 5 t ) V m E_x = 3\sin(5t) \hspace{0.2cm} \frac{V}{m}

Determine the maximum kinetic energy of the particle (in Joules, to 2 decimal places).

Note: All physical quantities are in standard SI units.

Inspiration .


The answer is 0.72.

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Steven Chase by Steven Chase , 37, USA

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2 solutions

Steven Chase
Oct 21, 2016

Analytical derivation and numerical simulation yield the same result (0.72 Joules).

6 Helpful 0 Interesting 0 Brilliant 0 Confused
Prakhar Bindal
Nov 14, 2016

Its very obvious that electric force is varying as restoring force varies in a spring block system.

So maximum velocity is at extreme ie where force changes its direction. its clear force will change direction at t=pi/5 as sin will change its sign

Now use a = qE/ m = dv/dt

Integrate to get v at t= pi/5

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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