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)

${\overrightarrow{F}}_{\text{e}}+{\overrightarrow{F}}_{\text{m}}=0\Rightarrow F_{\text{e}}=F_{\text{m}}\Rightarrow \text{eE}=\text{eVB}$
$v=\frac{E}{B}\Rightarrow \frac{\text{3.2}\times 10^5}{2\times 10^{-3}}=\text{1.6}\times 10^{8}m{s}^{-1}$
$r=\frac{mv}{qB}=\frac{\text{9.1}\times 10^{-3}\times \text{1.6}\times 10^8}{\text{1.6}\times 10^{-19}\times 2\times 10^{-3}}=\text{0.45 m}$