Electromagnetism - particle moving in magnetic field

[latentcorpse]

v(t)=\frac{D(t)}{r} where D(t) is some polynomial in t?

 

[gabbagabbahey]

If the radial part is zero, doesn't that mean \frac{mv^2-Bvqr}{qr}=0...solve that for v

 

[kof9595995]

refer to the feyman lectures on physics Vol 2 chapter17-3

 

[latentcorpse]

for a non trivial solution v(t)=\frac{B(r,t)q^2r^2}{m}

i still don't really see what to do next though?

 

[gabbagabbahey]

for a non trivial solution v(t)=\frac{B(r,t)q^2r^2}{m}

i still don't really see what to do next though?

First, check your algebra because this result is a little off...second calculate dv/dt and hence find the tangential component of E...then check to see if E satisfies Gauss' Law (use the differential form) and Faraday's law (use the integral form).

 

[latentcorpse]

v(t)=\frac{B(r,t)qr}{m}

\Rightarrow \frac{d v(t)}{dt}=\frac{qr}{m} \frac{\partial{B(r,t)}}{\partial{t}}

therefore the tangential component of E is E_{\phi}=r\frac{\partial{B(r,t)}}{\partial{t}}


shall i just take a gaussian pillbox to test both Gauss and Faraday?

 

[gabbagabbahey]

shall i just take a gaussian pillbox to test both Gauss and Faraday?

Why use the integral form of Gauss' law? Since you now know E (or at least have made a guess at what E is), just take the divergence of it.

And Faraday's law requires a loop, not a surface.