Home
Class 12
PHYSICS
Find the electric field at the centre of...

Find the electric field at the centre of a uniformly charged semicircular ring of radius R. Linear charge density is `lamda`

Text Solution

Verified by Experts

We split the semicircular arc into small segments ds. We have point charge on each segment as `lambdads`. The electric field due to this small segment of charges, from Coulomb's law,
`dE=(1)/(4piepsilon_(0))(lambdads)/(R^(2))`
Each little portion of the arc will give dE, in a different direction. We must therefore take components in order to find the total field at the centre.
Here X-component of the electric field is zero. This is the result of the fact that `dE_(x)` shown in the figure will be cancelled by the contribution from a symmetrically placed ds on the left half of the arc.
Hence we need only to compute `dE_(y)` which is vertically downward.
`dE_(y)=(lambdadscostheta)/(4piepsilon_(0)R^(2))=(lambda(Rd theta)costheta)/(4piepsilon_(0)R^(2))`
`E_(y)=intdE_(y)=(lambda)/(4piepsilon_(0)R)underset(-pi//2)overset(pi//2)intcosthetad theta=(lambda)/(2piepsilon_(theta)R)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Electric field at centre of a uniforly charged semicirlce of radius a is

Find the centre of mass of a uniform semicircular ring of radius R and mass M .

Find the electric field at centre of semicircular ring shown in figure . .

Electric field at centre O of semicircule of radius 'a' having linear charge density lambda given is given by

Electric field at the centre of uniformly charge hemispherical shell of surface charge density sigma is (sigma)/(n epsi_(0)) then find the value of n .

The electric field at 2R from the centre of a uniformly charged non - conducting sphere of rarius R is E. The electric field at a distance ( R )/(2) from the centre will be

(a) Using Gauss's law, derive an expression for the electric field intensity at any point outside a uniformly charged thin spherical shell of radius R and charge density sigma C//m^(2) . Draw the field lines when the charge density of the sphere is (i) positive, (ii) negative. (b) A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of 100 mu C//m^(2) . Calculate the (i) charge on the sphere (ii) total electric flux passing through the sphere.

Electric field at a point of distance r from a uniformly charged wire of infinite length having linear charge density lambda is directly proportional to

Find the electric field due to an infinitely long cylindrical charge distribution of radius R and having linear charge density lambda at a distance half of the radius from its axis.

A point charge q_(0) is placed at the centre of uniformly charges ring of total charge Q and radius R. If the point charge is slightly displaced with negligible force along axis of the ring then find out its speed when it reaches a large distance.