Answer to Question #93430 in Electricity and Magnetism for MGM

Question

An electron and a proton, having the same kinetic energy, enter a region of uniform magnetic field moving perpendicular to the field. Calculate the ratio of the radii of their circular paths in the field.

Answer 1

According to Newton's second law, we can write

$r=\frac{mv} {Bq} (1)$

The speed is equal to

$v=\sqrt {\frac{2EK } {m} } (2)$

We put (2) in (1)

$\frac{r_p}{r_e}=\sqrt{\frac{m_p}{m_e}} (3)$

where m_p=1.67×10^-27 kg, m_e=9.1×10^-31 kg

 

Using (3) we got

$\frac{r_p} {r_e}=42.8$

Answer

42.8