Why is electric flux through ring same as that of electric flux through disc?

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The electric flux through a ring is the same as the electric flux through a disc, provided they both have the same radius and the same total charge enclosed within them. This is known as Gauss's law, which states that the electric flux through a closed surface is proportional to the charge enclosed within the surface.

To understand why this is the case, consider a ring and a disc of the same radius, centered on the same axis. Let us assume that both the ring and the disc have a total charge Q enclosed within them.

Ring and a Disc of Same Radius

Ring and a Disc of Same Radius

The electric flux through the ring can be found by considering a small element of the ring, which is essentially a strip of infinitesimal width.
The electric field at any point on this strip is perpendicular to the strip, and the magnitude of the electric field is given by Coulomb's law.
The total flux through the ring is then found by integrating the electric field over the entire ring.
Similarly, the electric flux through the disc can be found by considering a small element of the disc, which is essentially a circular patch of infinitesimal area.
The electric field at any point on this patch is perpendicular to the patch, and the magnitude of the electric field is given by Coulomb's law.
The total flux through the disc is then found by integrating the electric field over the entire disc.

Now, since the ring and the disc have the same radius and the same total charge enclosed within them, the magnitude of the electric field at any point on the ring or the disc will be the same. Therefore, the integral of the electric field over the entire ring will be the same as the integral of the electric field over the entire disc, and hence the electric flux through the ring and the disc will be the same.

Therefore, the electric flux through a ring is the same as the electric flux through a disc, provided they both have the same radius and the same total charge enclosed within them. This is because the magnitude of the electric field at any point on the ring or the disc will be the same, and the integral of the electric field over the entire ring or disc will also be the same.

Also check:

Important Concepts Related to Electric Flux
Continuous Charge Distribution	Unit of Electric Field	Physical Significance of Electric Field
C harge density formula	Parallel Combination of Resistances	Electric Charges and Fields

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Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

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The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

\( \frac{q}{4 \pi \epsilon_0 l^2} \) pointing along MA
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Why is electric flux through ring same as that of electric flux through disc?

CBSE CLASS XII Related Questions

1.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

3.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

4.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

5.
The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

6.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

Similar Physics Concepts

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Why is electric flux through ring same as that of electric flux through disc?

CBSE CLASS XII Related Questions

1.Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2. If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

3.Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

4.Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

5.The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

6.A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

3.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

4.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

5.
The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

6.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.