help@askiitians.com

1800-150-456-789

Electrostatics> A small particle of mass m and charge -q ...

question mark

A small particle of mass m and charge -q is placed at point P on the axis of uniformly charged ring and released. If R>>x, the particle will undergo oscillations along the axis of symmetry with an angular frequency that is equal to ?

Md Saif Akhtar , 8 Years ago

Grade 12

2 Answers

Shoubhik

Last Activity: 8 Years ago

We know that Electric field due to a ring is

: $E=\frac{kqx}{2(R^{2}+x^{2})^{3/2}}$

Let the charge $-q=$ $q_{0}$ for convenience,

so force acting on the charge is

$F=q_{0}E$

For small displacement:

$E=\frac{kqx}{2R^{3}}$

Restoring force acting on charge:

$F=Kx$

So by both equations we get,

$Kx=\frac{kqx}{2R^{3}}$

$=>K=\frac{kq}{2R^{3}}$

But

$K=m\omega ^{2}$

So,

$\omega=\sqrt{\frac{kq}{2mR^{3}}}$

Yash Shisode

Last Activity: 6 Years ago

E=(KQx)/(R^2 + x^2) ^3/2

As R>>>x, x^2

Therefore, E=(KQx)/R^3 -----------(1)

F=m(omega) ^2 x -----------------------(2)

F=qE -----------------------(3)

From 1,2&3

m(omega) ^2 x =( kqQx) /R^3

Omega = √(KqQ) /√(mR^3)

= √(qQ) /√(4π£mR^3) as K=1/4π£

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Ask a Doubt

Get your questions answered by the expert for free

Electrostatics question based on earthing of spherical shell

electrostatics

0 Answer Available

Last Activity: 2 Years ago

an object has a charge of 2c and gains 10^19 electrons. the net chaarge on the object becomes??

electrostatics

1 Answer Available

Last Activity: 3 Years ago

A wire with a linear charge density lambda forms a quarter of a cjrclenof radius R and is placed asa shown in thefigure with its centre of curvature at the origin O the electric field at O will be

electrostatics

0 Answer Available

Last Activity: 3 Years ago

Find the value of q so that system remains in equilibrium.. figure attached below

electrostatics

0 Answer Available

Last Activity: 3 Years ago

Find the value of q so that system remains in equilibrium

electrostatics

0 Answer Available

Last Activity: 3 Years ago

View all Questions