Question

Electrons emitted with negligible speed from an electron gun are accelerated through a potential difference V along the x-axis. These electrons emerge from a narrow hole into a uniform magnetic field of strength B directed along x-axis. Some electrons emerging at slightly divergent angles as shown in the Fig. These paraxial electrons are refocused on the x-axis at a distance-

• A. $\sqrt { \frac { 8 \pi ^ { 2 } m V } { e ^ { 2 } } }$
• B. $\sqrt { \frac { 2 \pi ^ { 2 } \mathrm { mV } } { \mathrm { eB } } }$
• C. $\sqrt { \frac { 4 \pi ^ { 2 } \mathrm { mV } } { \mathrm { eB } ^ { 2 } } }$
• D.

Answer 1

Answer: (A)

$\sqrt { \frac { 8 \pi ^ { 2 } m V } { e ^ { 2 } } }$

Answer 2

KE = $\frac { 1 } { 2 }$ mv² = eV

Ž mv = $\sqrt { 2 \mathrm { emV } }$

The electron will be refocused after travelling a distance = pitch of helix

= =