Home
Class 12
PHYSICS
Consider a uniform spherical charge dist...

Consider a uniform spherical charge distribution of radius `R_(1)` centred at the origin `O`. In this distribution a spherical cavity of radius `R_(2)`, centred at `P` with distance `OP = a = R_(1) - R_(2)` (fig) is made.If the electric field inside the cavity at position `vec(r )`, then the correct statement is

A

(a) `vecE` is uniform, its magnitude is independent of `R_2` but its direction depends on `vecr`

B

(b) `vecE` is uniform, its magnitude depends on `R_2` and its direction depends on `vecr`

C

(c) `vecE` is uniform, its magnitude is independent of a but its direction depends on `veca`

D

(d) `vecE` is uniform and both its magnitude and direction depend on `veca`

Text Solution

Verified by Experts

The correct Answer is:
D
Assume the cavity to contain similar charge distribution of positive and negative charge as the rest of sphere. Electric field at M due to uniformly distributed charge of the whole sphere of radius `R_1`

`vecE=(rho)/(3epsilon)vecr`
Electric field at M due the negative charge distribution in the cavity
`vecE_2=(rho)/(3epsilon)vec(MP)`
`:.` The toal electric field at M is
`vecE=vecE_1+vecE_2=(rho)/(3epsilon)vecr+(rho)/(3epsilon)vec(MP)`
`:.` `vecE=(rho)/(3epsilon)vecr+(rho)/(3epsilon)(veca-vecr)[:' vecr+vec(MP)=veca]`
`:.` `vecE=(rho)/(3epsilon)veca`
(d) is the correct option
Promotional Banner

Topper's Solved these Questions

  • ELECTROSTATICS

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise Subjective Problems|2 Videos

  • ELECTROSTATICS

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise Comprehension Based Questions|2 Videos

  • ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise JEE Main And Advanced|107 Videos

  • MODERN PHYSICS

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise MCQ (One Correct Answer|1 Videos

Similar Questions

Explore conceptually related problems

Consider a uniform spherical charge distribution of radius R_(1) centred at the orgin O . In this distribution a spherical cavity fo radius R_(2) , centred at P with distance OP = a = R_(1) - R_(2) (fig) is made.If the electric field inside the cavity at position vec(r ) , then the correct statement is

Consider a uniform spherical volume charge distribution of radius R. Which of the following graphs correctly represents the magnitude of the electric field E as a distance r from the center of the sphere ?

Inside a uniformly charged infinitely long cylinder of radius 'R' and volume charge density 'rho' there is a spherical cavity of radius 'R//2'. A point 'P' is located at a dsintance 2 R from the axis of the cylinder as shown. Then the electric field strength at the point 'P' is

Two spherical cavities of radii a and b are hollowed out from the interior of a neutral conducting sphere of radius R . At the center of each cavity , a point charge is placed . Call these charges q_(a) and q_(b) . The electric field inside the cavity of radius a at a distance r from the center of cavity is

A solid sphere having uniform charge density rho and radius R is shown in figure. A spherical cavity ofradius (R)/(2) is made in it. What is the potential at point O?

Consider a uniform charged sphere of charge density r and radius R.If the cavity of radius R/2is made inside the sphere and the removed part is again placed near the charge distribution as shown in the figure. If the electric field at the centre of the cavity is (rho R)/(n varepsilon_(0) find n .

7.Consider a uniform charged sphere of charge density p and radius R.If the cavity of radius R/2is made inside the sphere and the removed part is again placed near the charge distribution as shown in the figure.If the electric field at the centre of the cavity is (rho R)/(n varepsilon_(0)) find n .

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

Inside a uniform sphere of density rho there is a spherical cavity whose centre is at a distance l from the centre of the sphere. Find the strength of the gravitational field inside the cavity.

A solid sphere of mass M and radius R has a spherical cavity of radius R/2 such that the centre of cavity is at a distance R/2 from the centre of the sphere. A point mass m is placed inside the cavity at a distanace R/4 from the centre of sphere. The gravitational force on mass m is