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प्रश्न
A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using Gauss’s law, derive an expression for an electric field at a point outside the shell.
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उत्तर
According to Gauss law,
`epsi_0EointdA=q`
Where,
q is the point charge
E is electric field due to the point charge
dA is a small area on the Gaussian surface at any distance and
`epsi_0` is the proportionality constant
For a spherical shell at distance r from the point charge, the integral `ointdA` is merely the sum of all differential of dA on the sphere.
Therefore, `oint dA =4pir^2`
`epsi_0E(4pir^2) = q`
or `,E = q/(epsi4pir^2)`
Therefore, for a thin conducting spherical shell of radius R and charge Q, spread uniformly over its surface, the electric field at any point outside the shell is
`E = Q/(e_0 4pir^2)`
Where r is the distance of the point from the centre of the shell.
`E = q/(4piepsi_0r^2)`
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संबंधित प्रश्न
q1, q2, q3 and q4 are point charges located at points as shown in the figure and S is a spherical gaussian surface of radius R. Which of the following is true according to the Gauss' law?
The surface considered for Gauss’s law is called ______.
Which of the following statements is not true about Gauss’s law?
The Electric flux through the surface
 (i) |
 (ii) |
 (iii) |
 (iv) |
Five charges q1, q2, q3, q4, and q5 are fixed at their positions as shown in figure. S is a Gaussian surface. The Gauss’s law is given by `oint_s E.ds = q/ε_0`
Which of the following statements is correct?
If there were only one type of charge in the universe, then ______.
- `oint_s` E.dS ≠ 0 on any surface.
- `oint_s` E.dS = 0 if the charge is outside the surface.
- `oint_s` E.dS could not be defined.
- `oint_s` E.dS = `q/ε_0` if charges of magnitude q were inside the surface.
An arbitrary surface encloses a dipole. What is the electric flux through this surface?
If the total charge enclosed by a surface is zero, does it imply that the elecric field everywhere on the surface is zero? Conversely, if the electric field everywhere on a surface is zero, does it imply that net charge inside is zero.
In 1959 Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density N, which is maintained a constant. Let the charge on the proton be: ep = – (1 + y)e where e is the electronic charge.
- Find the critical value of y such that expansion may start.
- Show that the velocity of expansion is proportional to the distance from the centre.
