A proton and an alpha-particle are both accel | vedclass

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

Question

(A) The acceleration of a charged particle in a uniform electric field $E$ is given by $a = \frac{qE}{m}$.Since the particles start from rest $(u = 0)

Vedclass · Accepted Answer

$1: 1$

Vedclass · Answer

(A) The acceleration of a charged particle in a uniform electric field $E$ is given by $a = \frac{qE}{m}$.Since the particles start from rest $(u = 0)$, the velocity after time $t$ is $v = at = \left(\frac{qE}{m}ight)t$.According to the work-energy theorem, the work done $W$ by the electric field is equal to the change in kinetic energy $\Delta K$:$W = \Delta K = \frac{1}{2}mv^2$.Substituting the expression for $v$:$W = \frac{1}{2}m\left(\frac{qEt}{m}ight)^2 = \frac{q^2 E^2 t^2}{2m}$.Since $E$ and $t$ are the same for both particles, $W \propto \frac{q^2}{m}$.For a proton, $q_p = e$ and $m_p = m$. For an $\alpha$-particle, $q_\alpha = 2e$ and $m_\alpha = 4m$.Therefore, the ratio is:$\frac{W_p}{W_\alpha} = \left(\frac{q_p}{q_\alpha}ight)^2 \left(\frac{m_\alpha}{m_p}ight) = \left(\frac{e}{2e}ight)^2 \left(\frac{4m}{m}ight) = \left(\frac{1}{4}ight) 	imes 4 = 1: 1$.

$A$ proton and an $\alpha$-particle are both accelerated from rest in a uniform electric field. The ratio of work done by the electric field on the proton and the $\alpha$-particle in a given time is

Similar Questions

$A$ negatively charged particle $p$ is placed, initially at rest, in a constant, uniform gravitational field and a constant, uniform electric field as shown in the diagram. What, qualitatively, is the shape of the trajectory of the particle?

The kinetic energy of an electron which is accelerated through a potential of $100 \, V$ is:

An electron having charge '$e$' and mass '$m$' is moving in a uniform electric field $E$. Its acceleration will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module