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You can shled a charge from electrical f...

You can shled a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means ?

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Knowledge Check

  • A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m^' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if 2r lt x lt 2R

    A
    `(Gmm^')/(4(x-x)^2)`
    B
    `(Gmm^')/(x-x)^2`
    C
    `(Gmm^')/(x-r)^3`
    D
    `(2Gmm^')/(x-r)^2`

  • A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m^' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if x gt 2R

    A
    `(2GMm^')/(x-r)^2+(Gmm^')/(x+r)^2`
    B
    `(2GMm^')/(2(x-R)^2)+(2Gmm^')/(x+r)^2`
    C
    `(2GMm^')/(x+R)^2+(Gmm^')/(x+r)^2`
    D
    `(2GMm^')/(x-R)^2+(Gmm^')/(x-r)^2`

  • A hollow metal sphere of radius R is charged with a charge Q. The electric potential and intensity inside the sphere are respectively density p=A/R , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is

    A
    `(2Q)/(pia^2)`
    B
    `Q/(2pia^2`
    C
    `Q/(2pi(b^2-a^2))`
    D
    `(2Q)/(pi(b^2-a^2))`

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    A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics(c,e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (~ 15 billion years). From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of ). If its coincidence with the age of the universe were significant , what would this imply for the constancy of fundamental constants ?

    Answer carefully: (a) Two large conducting spheres carrying charges Q_(1) and Q_(2) are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q_(1),Q_(2)//4pi epsilon_(0)r^(2) , where r is the distance between their centres? (b) If Coulomb’s law involved 1//r^(3) dependence (instead of would Gauss’s law be still true ? (c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point? (d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical? (e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there? (f) What meaning would you give to the capacitance of a single conductor? (g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

    You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘death- well’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m ?

    A spherical conductor of radius 12 cm has a charge of 1.6 xx 10^(-7) C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?

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