Question

An electron and a proton enter a magnetic field at right-angle to the field with same kinetic energy. The correct statement is that :

• A. the trajectory of electron is less curved
• B. the trajectory of proton is less curved
• C. both are equally curved
• D. both move along straight line paths

Answer 1

Answer: (B)

the trajectory of proton is less curved

Since both have the same kinetic energy,

=> $\frac{1}{2}{m}_p{V}_p^2=\frac{m_e}{2}{V}_e^2$

Also, $m_p>m_e\to V_e>V_p$

$F_p=F_e$

$R=\frac{mV}{qB}=\frac{2\left(KE\right)}{\left(qB\right)V}$

if KE, q and B are same then $R\alpha \frac{1}{V}$

$V_e>V_p\Rightarrow R_p>R_e$

So, trajectory of proton has longer radius and hence less curved.