A proton with a kinetic energy of 2.0 , eV mo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The kinetic energy $K = 2.0 \, eV = 2.0 	imes 1.6 	imes 10^{-19} \, J = 3.2 	imes 10^{-19} \, J$.The velocity $v$ is given by $K = \frac{1}{2}m

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(C) The kinetic energy $K = 2.0 \, eV = 2.0 	imes 1.6 	imes 10^{-19} \, J = 3.2 	imes 10^{-19} \, J$.The velocity $v$ is given by $K = \frac{1}{2}mv^2$,so $v = \sqrt{\frac{2K}{m}} = \sqrt{\frac{2 	imes 3.2 	imes 10^{-19}}{1.6 	imes 10^{-27}}} = \sqrt{4 	imes 10^8} = 2 	imes 10^4 \, m/s$.The pitch $p$ of the helical path is given by $p = (v \cos 	heta) 	imes T$,where $T = \frac{2\pi m}{qB}$ is the time period.Substituting the values: $p = v \cos 60^{\circ} 	imes \frac{2\pi m}{qB}$.$p = (2 	imes 10^4) 	imes \frac{1}{2} 	imes \frac{2\pi 	imes 1.6 	imes 10^{-27}}{1.6 	imes 10^{-19} 	imes (\frac{\pi}{2} 	imes 10^{-3})}$.$p = 10^4 	imes \frac{2 	imes 10^{-27}}{10^{-19} 	imes 0.5 	imes 10^{-3}} = 10^4 	imes 4 	imes 10^{-5} = 0.4 \, m$.Converting to centimeters: $p = 0.4 	imes 100 = 40 \, cm$.

Similar Questions

$A$ charged particle in a uniform magnetic field $B = B_0 \hat{k}$ starts moving from the origin with velocity $v = 3 \hat{i} + 4 \hat{k} \text{ m/s}$. The trajectory of the particle and the time $t$ at which it reaches $2 \text{ m}$ above the $x-y$ plane are,

An electron having mass $m$ and kinetic energy $K$ enters a uniform magnetic field $B$ perpendicularly. Its frequency will be:

In a crossed field, the magnetic field induction is $2.0 \,T$ and electric field intensity is $20 \times 10^3 \,V/m$. At which velocity will the electron travel in a straight line without being deflected by the electric and magnetic fields?

$A$ charge of $2.0\,\mu C$ moves with a speed of $3.0 \times 10^6\,m/s$ along the positive $X$-axis. $A$ magnetic field of strength $\vec B = -0.2\,\hat k\,T$ exists in space. What is the magnetic force $(\vec F_m)$ on the charge?

Vedclass Test Series

Exam Paper Generator

Online Exam Module