Solving a Particle's Radiating Force Under Force F

[hhhmortal]

Homework Statement

At time t = 0 a particle of charge 'q' and mass 'm' is at a position x = 0 and has a velocity v = 0. The particle is subject to a force F = k x^(1/2) , where 'k' is a constant. Show that at time 't' the particle radiates according to:

-dW/dt = q²k⁴t⁴ / (864)(π)(ε_0 )(c³)(m⁴)

The Attempt at a Solution

I first said F= ma = k x^1/2

--> a = k x^(1/2) / m

---> a² = k² x / m²


Then I substitute this into the larmor formula, but obviously this is wrong. I'm not sure where I went wrong though.

Thanks.

 

[gabbagabbahey]

---> a² = k² x / m²


Then I substitute this into the larmor formula, but obviously this is wrong. I'm not sure where I went wrong though.

What makes you so certain that this is wrong? Remember, the particle is accelerating along the x-direction, so its x-coordinate will be a function of time. You can find the exact form of x(t) by solving the differential equation \frac{d^2 x}{dt^2}=a.