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A positively charge sphere of radius r0 ...

A positively charge sphere of radius `r_0` carries a volume charge density `rho`. A spherical cavity of radius `r_0//2` is then scooped out and left empty. `C_1` is the center of the sphere and `C_2` that of the cavity. What is the direction and magnitude of the electric field at point B?

A

`(17rhor_0)/(54epsilon_0)`left

B

`(rhor_0)/(6epsilon_0)` left

C

`(17rhor_0)/(54epsilon_0)`right

D

`(rhor_0)/(6epsilon_0)`right

Text Solution

Verified by Experts

The correct Answer is:
A
a. Electric field on surface of a uniformly charged sphere is given
by
`Q/(4piepsilon_0R^2) = (rhoR)/(3epsilon_0)`
Electric field at outside point is given by
`E = Q/(4piepsilon_0r^2) = (rhoR^3)/(3epsilon_0r^2)`
`E_B = E_(whol e sphere) - E_(cavity)`
`= (rhor_0)/(3epsilon_0) - (rho(r_0/2)^3)/(3epsilon_0(3r_0/2)^2) = (17rhor_0)/(54epsilon_0)`.
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Knowledge Check

  • A positively charged sphere of radius r_(0) carries a volume charge density rho_(E) (Figure). A spherical cavity of radius r_(0)//2 is then scooped out and left empty, as shown. What is the direction and magnitude of the electric field at point B?

    A
    `(17rhor_(0))/(54in_(0)) l eft`
    B
    `(rho_(0))/(6in_(0))l eft`
    C
    `(17rhor_(0))/(54in_(0))right`
    D
    `(rhor_(0))/(6in_(0)) right`

  • A solid non-conducting sphere of radius R is charged with a uniform volume charge density rho . Inside the sphere a cavity of radius r is made as shown in the figure. The distance between the centres of the sphere and the cavity is a. An electron of charge 'e' and mass 'm' is kept at point P inside the cavity at angle theta = 45^(@) as shown. If at t = 0 this electron is released from point P, calculate the time it will take to touch the sphere on inner wall of cavity again.

    A
    `sqrt((3Rm epsilon_(0)r)/(e rho a))`
    B
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    D
    `sqrt((6sqrt(2)m epsilon_(0)r)/(e rho a))`

  • The figure represents a solid uniform sphere of mass M and radius R . A spherical cavity of radius r is at a distance a from the centre of the sphere. The gravitational field inside the cavity is

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    All of these

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