How Long for an Electron's Energy to Decrease Tenfold in a Magnetic Field?

[Maximtopsecret]

Homework Statement

Electron e, mass m, moves in constant homogeneous magnetic field H. Find time interval for electron's energy to decrease 10 times due to emission.

Homework Equations

I know for sure from the class that m*a=(e/c)*(v⊥)*H (Lorentz force); intensity -I=dE/dt=-2e⁴v⊥²H²/(3m²c⁵)
dE/dt=(m/2)*d(v⊥²)/dt;
here we have d(v⊥²)/dt=-4e⁴v⊥²H²/(3m³c⁵)

The Attempt at a Solution

The problem is in the next step. What should I do further? I have a differential equation. May I take an integral over d(v⊥²) from v² to v²/10 and on the other side of equation take an integral over dt from 0 to t?[/sup]

 

[mfb]

After rearranging, you can do that.