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10^(12)alpha- particles (Nuclei of heliu...

`10^(12)alpha`- particles (Nuclei of helium) per second falls on a neutral sphere, calculate time in which sphere gets charged by `2mu C`.

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6.25
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The atomic weight of radius is 226. It is observed that 3.67 xx 10^(10) " " alpha- particles are emitted per second from one gram of radium. Calculate in years the half period of radium.

There is a fixed sphere of radius R having positive charge Q uniformly spread in its volume. A small particle having mass m and negative charge (– q) moves with speed V when it is far away from the sphere. The impact parameter (i.e., distance between the centre of the sphere and line of initial velocity of the particle) is b. As the particle passes by the sphere, its path gets deflected due to electrostatics interaction with the sphere. (a) Assuming that the charge on the particle does not cause any effect on distribution of charge on the sphere, calculate the minimum impact parameter b0 that allows the particle to miss the sphere. Write the value of b_(0) in term of R for the case 1/2mV^(2)=100.((kQq)/(R)) (b) Now assume that the positively charged sphere moves with speed V through a space which is filled with small particles of mass m and charge – q. The small particles are at rest and their number density is n [i.e., number of particles per unit volume of space is n]. The particles hit the sphere and stick to it. Calculate the rate at which the sphere starts losing its positive charge (dQ)/(dt). Express your answer in terms of b_(0)

Knowledge Check

  • A spherical capacitor has an inner sphere of radius 10 cm and outer sphere of radius 12 cm . The outer sphere is earthed and the inner sphere is given a charge of 5 mu C . The capacitance of the capacitor is

    A
    `2.40 ( pi epsilon_(0))`
    B
    `4.80 ( pi epsilon_(0))`
    C
    `2.00 ( pi epsilon_(0))`
    D
    ` 3.00 ( pi epsilon_(0))`

  • The number of alpha particles emitted per second by 1g of 88^226 Ra is 3.7 times 10^10 . The decay constant is :

    A
    `1.39 times 10^-11 sec^-1`
    B
    `13.9 times 10^-11 sec^-1`
    C
    `139 times 10^-10 sec^-1`
    D
    `13.9 times 10^-10 sec^-1`

  • A conducting sphere carries a net charge of -6 mu C . The sphere is located at the center of a conducting spherical shell that carries a net charge of +2 mu C as shown in the figure. Determine the excess charge on the outer surface of the spherical shell.

    A
    `-4 mu C`
    B
    `+4 mu C`
    C
    `- 8 mu C`
    D
    `+8 mu C`

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    A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere si earthed and the inner sphere is given a charge of 2.5 muC . The space between the concentric spheres is filled with a liquid of dielectric constant 32. (a) Determine the capacitance of the capacitor. (b) What is the potential of the inner sphere ? (c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm.Explain why the latter is much smaller ?

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