Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

  • Complete Physics Course - Class 11
  • OFFERED PRICE: R 2,800
  • View Details
Get extra R 700 off


consider a uniformly charged ring of radius R.Find the point on the axis where the elecrtic field is maximum.

6 years ago


Answers : (3)


let the total charge on the ring is Q then

electric field at the axis of a charged ring is given by

      E=kQx/(R2 + x2)3/2                

   to find maximum electric field we can use the concept of maxima and minima....

 dE/dx = d/dx of {kQx/(R2 + x2)3/2 }

          =kQ{  1 .(R2 +x2)3/2 - 3/2 (R2 +x2)1/2. x }/(R2 +x2)3                 (by applying quotient rule)

now on putting dE/dx =0 ,we get

      x2 -3x/2+R2 =0

      x2 -3x/2 +9/16  -9/16  +R2  =0            

       (x-3/4)2 = 9/16-R2

        x={(9-16R2)1/2 +3 }/4   units

 therefore at a distance x from center of the ring electric field is maximum.......

6 years ago

Hello raju....


This is very simple...Just it needs a few steps of derivation...I am solving it with derivation...from the begining Let me know if u get stick with any line ....


It is :

Electric field due to:

 Charged ring of charge Q and radius R.

1) The Center=0.

Linear charge density (l) on ring =

Consider the field at center due to any element =

But the field due to point diametrically opposite = in opposite direction.
Net field at center = 0 (By symmetry)

2)      On the axis =

On axis of ring at distance x.
                                  Fig (5)

As obvious from the diagram the field component along the line gets added due to opposite element.



Now ...We have to find at which  x the field is calculate dE/dx ...


dE/dx = Z [ (R^2 + x^2)^3/2  - 3/2(R^2+x^2)^1/2 . 2(x).(x) ] / [R^2+x^2]^3   ; where Z = Q/4pi*epsilon


For maximum let dE/dx = 0


then ..(R^2x +x^2)^3/2 - 3x^2(R^2+x^2)^1/2 = 0

(R^2 +x^2)^1/2 [ (R^2 +x^2) - 3x^2 ] = 0


hence ...R^2 = 2x^2


or .... x = + R/root(2)   or - R/root(2)


Means If ring is kept symmetrically in x-y plane with center at origin then..field will be maximum at ...a distance ..of +R/root(2) above the +z-axis...and below the negative z axis...


Is it clear


With regards



6 years ago


2 years ago

Post Your Answer

Other Related Questions on Electrostatics

an infinite line charge passes through a cube. what is the minimum and maximum flux throgh the cube?
As from Gauss's law flux is defined as Flux = E.ds = q(total)/e Flux = ql/e For maximum flux, l = aroot3 For minium flux l = a Hence maximum and minimum fluxes are defined respectively =>...
Vikas TU 11 days ago
is it possible to create magnetic field without electric field?
@ krishna there are 2 way of creating an electric field , – introduce an electrically charged particle , or introduce a time varying magnetic field . however , there are no magnetically...
Umakant biswal one month ago
hiii i find difficult in this chapter plz tell a easy way to get grip on ths topic plz help in ths regard.
About which chapter you are talking about? Can you please mention it.
Vijay Mukati 6 months ago
Please mention the chapter
Harsh Patodia 6 months ago
a ball is projected with a velocity of 40√2 m/s at an angle of 45 find the position and velocity of the ball after 2 sec
please explain further in an easier way
the 3 months ago
velocity in both x and y directions=40 m/s. For X coordinate, X=40t i.e X=40x2=80m For Y coordinate, Y=Uyt+1/2gt^2 i.e. Y=40x2-1/2x10x4=60m Position of ball after 2 sec= (80,60) Velocity in ...
Prabhjot Singh 3 months ago
if the focal of a convex lens is 20cm what is its power in dioptres
sai kumar one year ago
mr venky, It is 5 Diopters since power=1/f........
Gowri sankar 9 months ago
it is 5 Diopters since power=1/f
Mondo Camry one year ago
Q 17 plz asap plz also tell me how to find out torque direction
@ manas you can calculate the value of torque by the following formula that is = torque = force * perpendicular distance . and the direction of torque are the same as that of the magnetic...
Umakant biswal 4 months ago
torque is herently a vector quantity.part of the torque calculation is the determination of the direction.the direction perpendicular to the radius both of the axis of the axis.
kumar 4 months ago
View all Questions »

  • Complete Physics Course - Class 12
  • OFFERED PRICE: R 2,600
  • View Details
Get extra R 650 off

  • Complete Physics Course - Class 11
  • OFFERED PRICE: R 2,800
  • View Details

Get extra R 700 off

More Questions On Electrostatics

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details