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Two concentric rings, one of radius a an...

Two concentric rings, one of radius a and the other of radius b, have the charges +q, and `-(2//5)^(-3//2)q`, respectively as shown in fig.

Find the ratio `b//a` if a charge particle placed on the axis at z =a is in equilibrium.

Text Solution

Verified by Experts

The correct Answer is:
2
For the equilbrium of charge at z=a, the net electric field at this point due to both the rings should be zero.
`E_(A)+E_(B)=0implies(kq_(A)a)/((a^(2)+a^(2))^(3//2))+(kq_(B)a)/((b^(2)+a^(2))^(3//2))=0`
Put the value and solve to get `b//a=2`.
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Knowledge Check

  • Two concentric conducting shells of radius a and (gt a) carry charges Q and -2Q respectively. The correct variation of electric intensity E as a function of r is given by

    A
    B
    C
    D

  • Two identical coaxial rings each of radius R are separated by a distance of sqrt3R . They are uniformly charged with charges +Q and -Q respectively. The minimum kinetic energy with which a charged particle (charge +q ) should be projected from the centre of the negatively charged ring along the axis of the rings such that it reaches the centre of the positively charged ring is

    A
    `(Qq)/(4piepsilon_0R)`
    B
    `(Qq)/2piepsilon_0R)`
    C
    `(Qq)/(8piepsilon_0R)`
    D
    `(3Qq)/(4piepsilon_0R)`

  • Two concentric rings, one of radius R and total charge +Q and second of radius 2R and total charge -sqrt(8)Q , lie in x-y plane (i.e., z=0 plane). The common centre of rings lies at origin and the common axis coincides with z -axis. The charge is uniformly distributed on both rings. At what distance from origin is the net electric field on z -axis zero?

    A
    `(R )/(2)`
    B
    `(R )/(sqrt(2))`
    C
    `(R )/(2sqrt(2))`
    D
    `sqrt(2)R`