A proton and an alpha-particle having equal k | vedclass

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

Question

(B) The force on a charged particle in an electric field is given by $F = qE$,where $q$ is the charge and $E$ is the electric field intensity.The acce

Vedclass · Accepted Answer

$\alpha$-particle trajectory is more curved.

Vedclass · Answer

(B) The force on a charged particle in an electric field is given by $F = qE$,where $q$ is the charge and $E$ is the electric field intensity.The acceleration of the particle is $a = \frac{F}{m} = \frac{qE}{m}$.For a particle moving with initial velocity $v$ perpendicular to the electric field,the deflection $y$ after traveling a horizontal distance $x$ is given by $y = \frac{1}{2} a t^2 = \frac{1}{2} (\frac{qE}{m}) (\frac{x}{v})^2 = \frac{qE x^2}{2 m v^2}$.Since the kinetic energy $K = \frac{1}{2} m v^2$ is constant,we can write $m v^2 = 2K$. Substituting this into the deflection equation,we get $y = \frac{qE x^2}{4K}$.For a proton,$q_p = e$. For an $\alpha$-particle,$q_{\alpha} = 2e$. Since both have the same kinetic energy $K$ and are in the same electric field $E$,the deflection $y$ is directly proportional to the charge $q$.Since $q_{\alpha} > q_p$,the deflection of the $\alpha$-particle is greater than that of the proton. Therefore,the $\alpha$-particle trajectory is more curved.

$A$ proton and an $\alpha$-particle having equal kinetic energy are projected into a uniform transverse electric field as shown in the figure.

Similar Questions

An electron of mass $m_e$ and a proton of mass $m_p$ are kept in a uniform electric field. The ratio of the acceleration of electron $(a_e)$ to the acceleration of proton $(a_p)$ is

The electric field at a point is given by $\vec E = E_0 \hat i \, V/m$. $A$ particle of charge $+q_0$ moves from point $A(0, a)$ to $B(a, 0)$ along a circular path as shown in the figure. Find the work done by the electric field in this motion.

Two charged particles of masses in the ratio $1: 3$ have charges in reciprocal ratio as their masses. They are placed in a uniform electric field and allowed to move. The ratio of their kinetic energies is

Kinetic energy of an electron accelerated in a potential difference of $100 \, V$ is

The tiny ball at the end of the thread shown in the figure has a mass of $0.5 \, g$ and is placed in a horizontal electric field of intensity $500 \, N/C$. It is in equilibrium in the position shown. The magnitude and sign of the charge on the ball is .....$\mu C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module