Question

A particle having charge q enters in a region of uniform magnetic field (directed inward) and get deflected by x after traveling a distance y. The magnitude of momentum of the particle is–

• A. $\frac { \mathrm { qBy } } { 2 }$
• B. $\frac { \mathrm { qBy } } { \mathrm { x } }$
• C. $\frac { q B } { 2 } \left( \frac { y ^ { 2 } } { x } + x \right)$
• D.

Answer 1

Answer: (C)

$\frac { q B } { 2 } \left( \frac { y ^ { 2 } } { x } + x \right)$

Answer 2

R = ... (1)

mv = qBR ... (2)

(R – x)² + y² = R² (Pythagoras) ... (3)

R² + x² – 2xR + y² = R² ... (4)

R = $\frac { x ^ { 2 } + y ^ { 2 } } { 2 x }$ From (2) and (4) mv = qB

P = $\frac { q B } { 2 }$ $\left( \frac { y ^ { 2 } } { x } + x \right)$