Question

An electron of mass $0.90\times {10}^{-30}$ kg under the action of a magnetic field moves in a circular of 2.0 cm radius at a speed of $3.0\times {10}^{6}m{s}^{-1}$. If a proton of mass $1.8\times {10}^{27}$ kg was to move in a circle of the same radius in the same magnetic field, then its speed will be

• A. $3.0\times {10}^{6}m{s}^{-1}$
• B. $1.5\times {10}^{3}m{s}^{-1}$
• C. $6.0\times {10}^{4}m{s}^{-1}$
• D. cannot be estimated from the given data

Answer 1

Answer: (B)

$1.5\times {10}^{3}m{s}^{-1}$

$mv=qBr$
$B$ and $r$ are same for both electron and proton.
$q$ is numerically same for both.
$\therefore mv=constant$
$\therefore m_p{v}_p=m_e{v}_e$

$\Rightarrow v_p=\frac{m_e{v}_e}{m_p}$
$=\frac{0.9\times {10}^{-30}\times 3\times {10}^6}{1.8\times {10}^{-27}}$
$=1.5\times {10}^{3}m/s$