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A ring of radius R carries a unif...

A ring of radius R carries a uniformly distributed charge ` + Q. ` A point charge ` - q ` is placed on the axis of the ring at a distance ` 2R ` from its centre and than released. Will the charge -q execute a simple harmonic motion along the axis of the ring ?

Text Solution

Verified by Experts

In this case, it can be shown that the force on the point charge -q is inversely proportional to the square of its distance from the centre of the ring. This is not the characteristics of a simple harmonic motion. So the particle will not execute a simple harmonic motion.
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Knowledge Check

  • A ring of radius R carries a charge +q . A test charge -q_0 is released on its axis at a distance sqrt3 R from its centre. How much kinetic energy will be acquired by the test charge when it reaches the centre of the ring ?

    A
    `1/(4piepsilon_0)(qq_0)/R`
    B
    `1/(4piepsilon_0)((qq_0)/(2R))`
    C
    `1/(4piepsilon_0)((qq_0)/(sqrt3R))`
    D
    `1/(4piepsilon_0)((qq_0)/(3R))`

  • A long straight wire of radius R carries a steady current whichis uniformly distributed through the cross section of the wire the magnitudes of the magnetic field at distance r_1 and r_2 from the centre of the wire are B_1 and B_2 respectively then

    A
    `B_1/B_2=(r_1)/(r_2).if r_1ltRand r_2ltR`
    B
    `B_1/B_2=(r_1)/(r_2).if r_1gtRand r_2gtR`
    C
    `B_1/B_2=(r_1)/(r_2).if r_1ltRand r_2ltR`
    D
    none of these

  • A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point 0 lying at distance L from the end A is

    A
    `Q/(8piin_0L)`
    B
    `3Q/(4piin_0L)`
    C
    `3Q/(4piin_0ln2)`
    D
    `(QIn2)/(4piin_0L)`

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