Question

A particle having charge $q$ enters a region of uniform magnetic field $\overrightarrow{B}$ (directed inwards) and is deflected a distance $x$ after travelling a distance $y$. The magnitude of the momentum of the particle is

• A. $\frac{qBy}{2}$
• B. $\frac{qBy}{x}$
• C. $\frac{qB}{2}(\frac{y^2}{x}+x)$
• D. $\frac{qB{y}^2}{2x}$

Answer 1

The correct option is C $\frac{qB}{2}(\frac{y^2}{x}+x)$

For a charged particle in magnetic field, radius of path is $R=\frac{p}{qB}$





From $△OCA$
$OA=2R\sin \theta =\sqrt{y^2+x^2}$
$\frac{2R.x}{\sqrt{y^2+x^2}}=\sqrt{y^2+x^2}$
$\frac{2p}{qB}=\frac{y^2+x^2}{x}$
$p=\frac{qB}{2}(\frac{y^2}{x}+x)$