Question

An infinitely long positively charged straight wire has a linear charge density λ. An electron is revolving around the wire as its centre with a constant speed in a circular plane perpendicular to the wire. Deduce the expression for its kinetic energy.

Answer 1

Let r be the radius of the uniform circular motion of the electron. The electric field intensity \(\vec E\) at every point on the circular path is radially outward and has the same magnitude E = \(\cfrac{λ}{2πεr}\).

∴ The centripetal force on the electron,

where m_e and v are the mass and linear speed of the electron.

∴ m_ev² = \(\cfrac{eλ}{2πε}\)

∴ The kinetic energy of the electron,

\(\cfrac12\) m_ev² = \(\cfrac{eλ}{4πε}\)