Question

A point charge q is placed at the centre of a circular wire of radius r having charge force of electrostatic interaction between point charge and the wire is:

Answer 1

Dear Student

A point charge Q is placed at the centre of a circular wire P of radius R having charge q.

The force of electrostatic interaction between point charge and the wire can be given as

F⃗ =QE⃗

NowCharge per unit length of

semicorcular wire λ=qπR

Charge on small element = dq =λRdθ

The electric field at the centre P of the semicircle wire is given bydE= kdqR2=kλRdθ

It is directed radially inwards for λ>0Now componets of dE⃗ is dEx= dE cosθ, dEy=− dE sinθSo total electric field is Ex =kλR∫π0cos θ dθ= kλR[sin θ]π0=0EY =−kλR∫π0sin θ dθ= kλR[cos θ]π0=−2kλRF=−2QkλR=−2QkR(qπR)=−2QqkπR2

Hope u understood well...........