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Calculate potential on the axis of a rin...

Calculate potential on the axis of a ring due to charge Q uniformly distributed along the ring of readius R.

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Calculate potential on the axis of a disc of radius R due to a charge Q uniformly distributed on its surface.

Calculate potential energy of a point charge -q placed along the axis due to a charge +Q uniformly distributed along a ring of radius R. Skecth P.E. as a function of a axial distance z from the center of the ring, Looking at graph, can you see what happen if -q is displaced slighlty from the centre of the ring (along the axis) ?

Knowledge Check

  • A ring of radius R is placed in the plane with its centre at origin and its axis along the x-axis and having uniformly distributed positive charge.A ring of radius r( ltlt R) and coaxial with the larger ring is moving along the axis with constant velocity then the variation of electrical flux (phi) passing through the smaller ring with position will be best represented by :

    A
    B
    C
    D

  • A ring of radius R , made of an insulating material carries a charge Q uniformly distributed on it. If the ring rotates about the axis passing through its centre and normal to plane of the ring with constant angular speed omega , then the magnitude moment of the ring is

    A
    `QomegaR^(2)`
    B
    `(1)/(2)QomegaR^(2)`
    C
    `Qomega^(2)R`
    D
    `(1)/(2)Qomega^(2)R`

  • A ring of radius R is placed in the plane its centre at origin and its axis along the x-asis and having uniformly distributed positive charge. A ring of radius r(ltltR) and coaxial with the larger ring is moving along the axis with constant velcity , then the variation of electrical flux (phi) passing through the smaller ring with position will be best represent by :

    A
    B
    C
    D

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    In a free space, a thin rod carrying uniformly distributed negative charge -q is placed symmetrically along the axis of a tin ring of radius R varrying uniformly dostributed charge Q. The mass of the rod is m and length is l=2R . The ring is fixed and the rod is free to move. The rod is displaced slightly along the axis of the ring and then released. Find the period T to the small amplitude oscillations of the rod.

    Short electric dipole of dipole moment P is placed at the centre of a ring of radius R having charge Q uniformly distributed on its circumference. The dipole moment vector is along the axis of the ring. Find force on the dipole due to the ring.

    Both the ring and the conducting sphere are given the same charge Q . Determine the potential of the sphere. Assume that the centre of the sphere lies on the axis of th ring. Is it necessary that the charge on the ring be uniformly distributed to answer the above question ?

    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 .

    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?

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