First slide

Force on a charged particle moving in a magnetic field

Question

A proton of mass $1 .67 \times 10^{- 27} kg$ and charge $1 .6 \times 10^{- 19} C$ is projected with a speed of $2 \times 10^{6} m / s$ at an angle of 60° to the X-axis. If a uniform magnetic field of 0.104 T is applied along Y-axis, the path of proton is

Moderate

A

A circle of radius 0.2 m and time period $π \times 10^{- 7} s$
B

A circle of radius 0.1 m and time period $2 π \times 10^{- 7} s$
C

A helix of radius 0.1 m and time period $2 π \times 10^{- 7} s$
D

A helix of radius 0.2 m and time period $4 π \times 10^{- 7} s$

Solution

Path of the proton will be a helix of radius, $r = \frac{mvsin θ}{qB}$
$(where θ = Angle between \vec{B} and \vec{v})$
$\begin{array}{l} \Rightarrow r = \frac{1 .67 \times 10^{- 27} \times 2 \times 10^{6} \times \sin 30^{0}}{1 .6 \times 10^{- 19} \times 0 .104} \\ = 0 .1 m \\ Time period, T = \frac{2 πm}{qB} = \frac{2 π \times 1 .67 \times 10^{- 27}}{1 .6 \times 10^{- 19} \times 0 .104} \\ = 2 π \times 10^{- 7} s \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App