Question

An electron (mass = $9.1 \, \times \, 10^{- 31 \, }kg$ ; charge = $- \, 1.6 \, \times \, 10^{- 19} \, C$ ) experiences no deflection if subjected to an electric field of $3.2 \, \times \, 10^{5} \, V \, m^{- 1}$ and a magnetic field of $2.0 \, \times \, 10^{- 3} \, \, Wb \, m^{- 2}$ . Both the fields are normal to the path of electron and to each other. If the electric field is removed, then the electron will revolve in an orbit radius

• A. $45m$
• B. $4.5m$
• C. $0.45m$
• D. $0.045m$

Answer 1

Answer: (C)

$\overset{ \rightarrow }{F}_{\text{e}}+\overset{ \rightarrow }{F}_{\text{m}}=0\Rightarrow F_{\text{e}}=F_{\text{m}}\Rightarrow \textit{eE}=\textit{eVB}$
$v=\frac{E}{B}\Rightarrow \frac{\text{3.2} \times 1 0^{5}}{2 \times 1 0^{- 3}}=\text{1.6}\times 10^{8}ms^{- 1}$
$r=\frac{m v}{q B}=\frac{\text{9.1} \times 1 0^{- 3} \times \text{1.6} \times 1 0^{8}}{\text{1.6} \times 1 0^{- 1 9} \times 2 \times 1 0^{- 3}}=\text{0.45 m}$