But since areas differ by a factor of 4, the effective ratio simplifies to 2 : 1.
Advertisements
Advertisements
प्रश्न
A point charge is placed at the centre of a hollow conducting sphere of internal radius ‘r’ and outer radius ‘2r’. The ratio of the surface charge density of the inner surface to that of the outer surface will be ______.
रिकाम्या जागा भरा
Advertisements
उत्तर
A point charge is placed at the centre of a hollow conducting sphere of internal radius ‘r’ and outer radius ‘2r’. The ratio of the surface charge density of the inner surface to that of the outer surface will be 2 : 1.
Explanation:
When a point charge is placed at the centre of a hollow conducting sphere, an equal and opposite charge is induced on the inner and outer surfaces.
Since surface charge density (σ) = `Q/(4 pi R^2)`, it is inversely proportional to the square of radius.
Inner radius = r
Outer radius = 2r
`sigma_"inner" : sigma_"outer" = 1/r^2 : 1/((2 r)^2)`
= 4 : 1
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
संबंधित प्रश्न
A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q.
(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?
(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.
(a) Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by
`(vec"E"_2 - vec"E"_1).hat"n" = sigma/in_0`
Where `hat"n"` is a unit vector normal to the surface at a point and σ is the surface charge density at that point. (The direction of `hat"n"` is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is σ `hat"n"/in_0`
(b) Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.
[Hint: For (a), use Gauss’s law. For, (b) use the fact that work done by electrostatic field on a closed loop is zero.]
Define electrostatic potential at a point. Write its S.I. unit. Three-point charges q1, q2 and q3 are kept respectively at points A, B, and C as shown in the figure, Derive the expression for the electrostatic potential energy of the system.
Electric-field magnitude 'E' at points inside and outside a positively charged spherical conductor having charge Q and a radius R are ______.
If R is the radius of a spherical conductor, Vm the dielectric strength, then the maximum electric-field magnitude to which it can be raised is ______.
The electrostatic potential on the surface of a charged conducting sphere is 100V. Two statements are made in this regard S1 at any point inside the sphere, electric intensity is zero. S2 at any point inside the sphere, the electrostatic potential is 100 V. Which of the following is a correct statement?
A conductor carries a certain charge. When it is connected to another uncharged conductor of finite capacity, then the energy of the combined system is ______.
Which of the following statements is false for a perfect conductor?
Three Charges 2q, -q and -q lie at vertices of a triangle. The value of E and V at centroid of triangle will be ______.
A test charge q is made to move in the electric field of a point charge Q along two different closed paths (Figure). First path has sections along and perpendicular to lines of electric field. Second path is a rectangular loop of the same area as the first loop. How does the work done compare in the two cases?
