Question

An electron and a proton enter region of uniform magnetic field in a direction at right angles to the field with the same kinetic energy. They describe circular paths of radius $r _ { e }$ and $r _ { p }$ respectively. Then

• A. $r _ { e } = r _ { p }$
• B. $r _ { e } < r _ { p }$
• C. $r _ { e } > r _ { p }$
• D. $r _ { e }$ may be less than or greater than $r _ { p }$ depending on the direction of the magnetic field

Answer 1

Answer: (B)

$r _ { e } < r _ { p }$

Answer 2

$r = \frac { \sqrt { 2 m K } } { q B }$ i.e. $r \propto \frac { \sqrt { m } } { q }$

Here kinetic energy K and B are same.

$\therefore \frac { r _ { e } } { r _ { p } } = \sqrt { \frac { m _ { e } } { m _ { p } } } \times \frac { q _ { p } } { q _ { e } } \Rightarrow \frac { r _ { e } } { r _ { p } } = \sqrt { \frac { m _ { e } } { m _ { p } } } \left( \because q _ { e } = q _ { p } \right)$

Since m_e < m_p, therefore r_e < r_p