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A Charge ‘Q’ is Placed at the Centre of a Cube of Side L. What is the Electric Flux Passing Through Each Face of the Cube? - Physics

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प्रश्न

A charge ‘q’ is placed at the centre of a cube of side l. What is the electric flux passing through each face of the cube?

उत्तर

By using Gauss’s Law.

It is given as

`Phi = oint vecE*dvecs = q/in_0`

Now, the flux passing through all the six surfaces would be

`Phi = 6phi =q/in_0`

And the flux passing through each surface would be

`phi = q/(6in_0)`

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Gauss’s Law
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2011-2012 (March) All India Set 1

संबंधित प्रश्‍न

A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in the Figure. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.) 


Answer the following question.
State Gauss's law for magnetism. Explain its significance.


Answer the following question.
State Gauss's law on electrostatics and drive expression for the electric field due to a long straight thin uniformly charged wire (linear charge density λ) at a point lying at a distance r from the wire.


The Electric flux through the surface


(i)

(ii)

(iii)

(iv)

If `oint_s` E.dS = 0 over a surface, then ______.

  1. the electric field inside the surface and on it is zero.
  2. the electric field inside the surface is necessarily uniform.
  3. the number of flux lines entering the surface must be equal to the number of flux lines leaving it.
  4. all charges must necessarily be outside the surface.

If there were only one type of charge in the universe, then ______.

  1. `oint_s` E.dS ≠ 0 on any surface.
  2. `oint_s` E.dS = 0 if the charge is outside the surface.
  3. `oint_s` E.dS could not be defined.
  4. `oint_s` E.dS = `q/ε_0` if charges of magnitude q were inside the surface.

Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region

  1. the electric field is necessarily zero.
  2. the electric field is due to the dipole moment of the charge distribution only.
  3. the dominant electric field is `∞ 1/r^3`, for large r, where r is the distance from a origin in this region.
  4. the work done to move a charged particle along a closed path, away from the region, will be zero.

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.

  1. Find the critical value of y such that expansion may start.
  2. Show that the velocity of expansion is proportional to the distance from the centre.

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