A charge of magnitude q is distributed on semicircular thin non conductive wire of radius r such that half of the semi circle has a positive charge while other half has negative charge .The field at the centre of semi circle is

a)q/²₀r²

b)q/4²₀r²

c)q/2²₀r²

d)2q/²₀r²

An infinite long wire holds a charge density  on it.A finite wire of length L is placed normal to the long wire and has a charge q uniformly distributed over it.

The net force on the finite wire is _____

a)q[logL]/2₀L

b)2q[logL]/₀L

c)q[log2L]/₀L

d)none

the force stretching the wire will be the tension acting tangentially.if  is the angle between the tangential components , resolve the tension and integrate to find the force. 2dtsin/2=_{[ 0]}^{[ 2pir]} kdQq/r*r

                     2tsin/2=_{[ 0]}^{[ 2pir]} kdxQq/2 pi r*r*r       (since dQ=dxQ/2 pi *r)

 on integrating u'll have -----t=Qq/8 pi ₀ r*r                                      

 

In vacuum some change is distributed in the form of a sphere with radius 'a' obeying the condition  = (1-x/a) where x=instantaneous distance from the centre.Compute electric field as a function of x where x is less than 'a' and

when x=a

sin2a =?