help@askiitians.com

1800-150-456-789

Electrostatics> Consider a circular ring of radius 'r' un...

question mark

Consider a circular ring of radius 'r' uniformly charged with a linear charge density lemda .Find the electric potential at a point on the axis at a distance x from the centre of the ring .Using this expression for the potential, find the electric field at this poi

Tanmay kumar , 6 Years ago

Grade 12

1 Answers

Eshan

Last Activity: 6 Years ago

Dear student,

Distance of each infinitesimally small charge element on the ring from the given point is

$d=\sqrt{x^2+r^2}$
Hence total electric potential at that point= $V=\dfrac{1}{4\pi\epsilon_0}\dfrac{\int dq}{\sqrt{x^2+r^2}}=\dfrac{1}{4\pi\epsilon_0}\dfrac{\lambda( 2\pi r)}{\sqrt{x^2+r^2}}=\dfrac{\lambda r}{2\epsilon_0\sqrt{x^2+r^2}}$
Hence $E=-\dfrac{dV}{dx}=\dfrac{1}{2}\dfrac{\lambda r}{2\epsilon_0 (x^2+r^2)^{3/2}}.2x=\dfrac{\lambda rx}{2\epsilon_0(x^2+r^2)^{3/2}}$

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