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Potential on the axis of ring of radius 3R and at distance 4R from centre of ring is (charge on the ring is Q )

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A charge Q is uniformly on a ring of radius R . Find the electric potential on the axis of ring at distance x from the centre of the ring. Sketch variation of potential with respect to x .

Consider a uniformly charged ring of radius R and total charge Q. What is the magnitude of maximum possible electric field intensity on the axis of ring? What is the distance of point from the centre of ring at which the electric field is maximum?

Knowledge Check

  • The electric field strength due to a ring of radius R at a distance x from its centre on the axis of ring carrying charge Q is given by E = (1)/(4 pi epsilon_(0)) (Qx)/((R^(2) + x^(2))^(3//2)) At what distance from the centre will the electric field be maximum ?

    A
    `x = R`
    B
    `x = (R )/(2)`
    C
    `x = +- (R )/(sqrt(2))`
    D
    `x = sqrt(2) R`

  • An electric dipole is kept on the axis of a uniformly charged ring at distance d from the centre of the ring. The direction of the dipole moment is along the axis. The dipole moment is p , charge of the ring is Q & radius of the ring is R . The force on the dipole is

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

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