Two equal negative charges -q are fixed at th | vedclass

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

Question

(D) Let the positive charge $Q$ be at a general point $P(x, 0)$ on the $x-$ axis. The distance between each charge $-q$ and the charge $Q$ is $r = \sq

Vedclass · Accepted Answer

Execute oscillatory but not $SHM$

Vedclass · Answer

(D) Let the positive charge $Q$ be at a general point $P(x, 0)$ on the $x-$ axis. The distance between each charge $-q$ and the charge $Q$ is $r = \sqrt{a^2 + x^2}$.The electrostatic force exerted by each charge $-q$ on $Q$ is $F = \frac{1}{4 \pi \varepsilon_0} \frac{Qq}{a^2 + x^2}$.The components of these forces perpendicular to the $x-$ axis cancel each other out,while the components along the $x-$ axis add up.The net force on $Q$ is $F_{net} = 2F \cos 	heta$,where $\cos 	heta = \frac{x}{r} = \frac{x}{\sqrt{a^2 + x^2}}$.Substituting the values,we get $F_{net} = 2 \left( \frac{1}{4 \pi \varepsilon_0} \frac{Qq}{a^2 + x^2} ight) \left( \frac{x}{\sqrt{a^2 + x^2}} ight) = \frac{2 Qqx}{4 \pi \varepsilon_0 (a^2 + x^2)^{3/2}}$.Since the force $F_{net}$ is directed towards the origin (restoring force) and is not directly proportional to the displacement $x$ (due to the $(a^2 + x^2)^{3/2}$ term in the denominator),the motion is oscillatory but not simple harmonic motion $(SHM)$.

Two equal negative charges $-q$ are fixed at the points $(0, a)$ and $(0, -a)$ on the $y-$ axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $x-$ axis. The charge will

Similar Questions

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.

$A$ uniform electric field of $10^3 \, V/m$ is directed along the $y$-axis. $A$ particle of mass $1 \, g$ and charge $10^{-6} \, C$ is projected from the origin into the field with a velocity of $10 \, m/s$ along the positive $x$-axis. Its speed after $10 \, s$ is (in $m/s$):

An electron is moving towards the $x$-axis. If an electric field is applied along the $y$-direction,what is the path of the electron?

$A$ simple pendulum consists of a sphere with a mass of $8 \ \mu g$ and a charge of $39.2 \times 10^{-10} \ C$. When a horizontal electric field of $20 \times 10^3 \ V/m$ is applied,what angle (in degrees) does the string make with the vertical?

Vedclass Test Series

Exam Paper Generator

Online Exam Module