An electron is released from rest and falls under the influence of gravity. In the first centimeter, what fraction of the potential energy lost is radiated away?

Solution 12P

Step 1 of 4:

To determine the potential energy radiated by an accelerating electron

Let us consider an accelerating charged particle which radiates away energy

And if for a time ‘T’ , the magnitude of the acceleration is ‘a’, then the energy radiated is given by;

….(1)

Equation(1) is known as Larmor Formula.

Step 2 of 4:

Now let us consider a particle in its initial state of rest, then the kinetic energy of the particle for time ‘T’ is ,

….(2)