Consider a particle of mass 1 text{ g} and ch | vedclass

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

Question

(B) The force on the particle is $F = qE = qE_0 \sin(\omega t)$.Using Newton's second law, $ma = qE_0 \sin(\omega t)$, so $a = \frac{qE_0}{m} \sin(\om

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) The force on the particle is $F = qE = qE_0 \sin(\omega t)$.Using Newton's second law, $ma = qE_0 \sin(\omega t)$, so $a = \frac{qE_0}{m} \sin(\omega t)$.The velocity $v(t)$ is the integral of acceleration: $v(t) = \int a \, dt = \int \frac{qE_0}{m} \sin(\omega t) \, dt = -\frac{qE_0}{m\omega} \cos(\omega t) + C$.Since the particle starts from rest at $t = 0$, $v(0) = 0$, which gives $C = \frac{qE_0}{m\omega}$.Thus, $v(t) = \frac{qE_0}{m\omega} (1 - \cos(\omega t))$.The maximum speed occurs when $\cos(\omega t) = -1$, so $v_{\max} = \frac{2qE_0}{m\omega}$.Substituting the values: $q = 1 	ext{ C}$, $E_0 = 2 	ext{ N/C}$, $m = 1 	ext{ g} = 10^{-3} 	ext{ kg}$, and $\omega = 1000 	ext{ rad/s}$.$v_{\max} = \frac{2 	imes 1 	imes 2}{10^{-3} 	imes 1000} = \frac{4}{1} = 4 	ext{ m/s}$.

Similar Questions

The potential difference between two metal plates is $800 \, V$ and they are separated by a horizontal distance of $0.02 \, m$. $A$ particle of mass $1.96 \times 10^{-15} \, kg$ is held in equilibrium between the plates. If $e$ is the elementary charge,then the charge on the particle is .......

If an $\alpha$-particle and a proton are accelerated from rest by a potential difference of $1 \text{ MV}$,then the ratio of their kinetic energy will be

$A$ particle of charge $1\ \mu C$ and mass $1\ g$ moving with a velocity of $4\ m/s$ is subjected to a uniform electric field of magnitude $300\ V/m$ for $10\ s$. Then its final speed cannot be.......$m/s$.

$A$ mass $m = 20\,g$ has a charge $q = 3.0\,mC$. It moves with a velocity of $20\,m/s$ and enters a region of electric field of $80\,N/C$ in the same direction as the velocity of the mass. The velocity of the mass after $3\,s$ in this region is.......$m/s$.

The coordinates of $A, B, C$ and $D$ are $(a, b, 0), (2a, 0, 0), (a, -b, 0)$ and $(0, 0, 0)$ respectively. How much work is done in moving a charge $q$ from $A$ to $D$ in a uniform electric field $\vec{E}$ directed along the positive $x$-axis?

Vedclass Test Series

Exam Paper Generator

Online Exam Module