# Accelerating an electron in a betatron

**Electricity and Magnetism**Level 5

In a betatron, electrons move in circular orbits and are accelerated by a time dependent magnetic field, perpendicular to the plane of the orbits. Suppose that the flux through an orbit of radius \(r=25 \textrm{cm}\) grows during the acceleration time at a constant rate of \(\frac{d\Phi}{dt}=5 \textrm{Wb/s}\). In the acceleration process an electron in this orbit, acquires a kinetic energy \(\Delta{E_{k}}=25 \textrm{MeV}\). Find the distance covered **in meters** by the electron during the acceleration time. Keep in mind that that the radius of the electron's orbit does not change.

**Details and assumptions**

\[ e= 1.6 \times 10^{-19} C\] \[ 1\textrm{eV}= 1.6 \times 10^{-19} \textrm{J}\]