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Two coaxial rings, eacg of radius R, mad...

Two coaxial rings, eacg of radius R, made of thin wire are separated by a small distabce `l(l lt lt R)` and carry the charges `q` and `-q`. Find the electric field potential and strength at the axis of the system as a function of the x coordinate (see figure). Investigate these functions at `|x| gt gt R`

Text Solution

Verified by Experts

The correct Answer is:
`V=(ql)/(4 pi epsilon_(0))(X)/((R^(2)+X^(2))^(3//2))`
`E = -(ql)/(4 pi epsilon_(0))((R^(2)-2X^(2)))/((R^(2)+X^(2))^(5//2))`
`V = (kq)/(sqrt(R^(2)+(x-(l)/(2))^(2)))-(kq)/(sqrt(R^(2)+(x+(l)/(2))^(2)))`
`because x gt gtR` Dipole
`V = (kp)/(r^(2))=(kql)/(x^(2)) rArr E =(2kp)/(r^(2))=(2kql)/(x^(3))`.
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Knowledge Check

  • The maximum electric field intensity on the axis of a uniformly charged ring of charge q and radius R will be

    A
    `(1)/(4piepsilon_(0))(q)/(3sqrt(3)R^(2))`
    B
    `(1)/(4piepsilon_(0))(2q)/(3R^(2))`
    C
    `(1)/(4piepsilon_(0))(2q)/(3sqrt(3)R^(2))`
    D
    `(1)/(4piepsilon_(0))(3q)/(2sqrt(2)R^(2))`

  • Two thin wire rings each having a radius R are placed at a distance d apart with their axes coiciding. The charges on the two rings are +q and -q . The potential difference between the centres of the two rings is

    A
    (a) `(q)/(2pi in_0)[1/R-(1)/(sqrt(R^2-d^2))]`
    B
    (b) `(qR)/(4pi in_0d^2)`
    C
    (c) `(q)/(4pi in_0)[1/R-(1)/(sqrt(R^2+d^2))]`
    D
    (d) zero

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