Question

The maximum and minimum values of L such that velocity of emerging particle makes angle $\pi /3$ with the y-axis are

• A. $L_{min}=10cm,L_{max}=\infty$
• B. $L_{min}=20cm,L_{max}=40cm$
• C. $L_{min}=10cm,L_{max}=20cm$
• D. $L_{min}=20cm,L_{max}=\infty$

Answer 1

The correct option is D $L_{min}=20cm,L_{max}=\infty$

$\overrightarrow{v}=50\sqrt{3}\hat{i}+50\hat{j}$

$\therefore \parallel \overrightarrow{v}\parallel =\sqrt{(50\sqrt{3}{)}^2+{50}^2}=100$

$\sin \theta =\frac{L}{R}$ where $R=\frac{mv}{Bq}=\frac{50\times {10}^{-3}\times 100}{25\times 1}=\frac{1}{5}$

$\therefore L=\frac{1}{2}R=\frac{1}{2}\times \frac{1}{5}=\frac{1}{10}m=10cm$

Since the particle emerges from the field parallel to x-axis, the min
value of L is $AB+BC=R\cos {60}^{\circ }+R\cos {60}^{\circ }=2R\times \frac{1}{2}=R=20cm$

This is the min value of L.
The max value of L is $\infty$ as shown in the third figure.