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

CBSE CLASS XII Related Questions

1.
Assertion : Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more. Reason (R): Induced emf produced is directly proportional to the magnetic flux.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Both Assertion (A) and Reason (R) are false.

View Solution

2.
The magnetic field in a plane electromagnetic wave travelling in glass (\( n = 1.5 \)) is given by \[ B_y = (2 \times 10^{-7} \text{ T}) \sin(\alpha x + 1.5 \times 10^{11} t) \] where \( x \) is in metres and \( t \) is in seconds. The value of \( \alpha \) is:

\( 0.5 \times 10^3 \, \text{m}^{-1} \)
\( 6.0 \times 10^2 \, \text{m}^{-1} \)
\( 7.5 \times 10^2 \, \text{m}^{-1} \)
\( 1.5 \times 10^3 \, \text{m}^{-1} \)

View Solution

3.
Consider a cylindrical conductor of length \( l \) and area of cross-section \( A \). Current \( I \) is maintained in the conductor and electrons drift with velocity \( \vec{v}_d \, (|\vec{v}_d| = \frac{eE}{m} \tau) \), where symbols have their usual meanings. Show that the conductivity of the material of the conductor is given by \[ \sigma = \frac{n e^2 \tau}{m}. \]

View Solution

4.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

attract with a force \( \frac{F}{2} \)
repel with a force \( \frac{F}{2} \)
repel with a force \( F \)
attract with a force \( F \)

View Solution

5.
Nuclides with the same number of neutrons are called:

Isobars
Isotones
Isotopes
Isomers

View Solution

6.
In a Young's double-slit experiment, two waves each of intensity I superpose each other and produce an interference pattern. Prove that the resultant intensities at maxima and minima are 4I and zero respectively.

View Solution

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

CBSE CLASS XII Related Questions

1.
Assertion : Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more. Reason (R): Induced emf produced is directly proportional to the magnetic flux.

2.
The magnetic field in a plane electromagnetic wave travelling in glass (\( n = 1.5 \)) is given by \[ B_y = (2 \times 10^{-7} \text{ T}) \sin(\alpha x + 1.5 \times 10^{11} t) \] where \( x \) is in metres and \( t \) is in seconds. The value of \( \alpha \) is:

4.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

5.
Nuclides with the same number of neutrons are called:

6.
In a Young's double-slit experiment, two waves each of intensity I superpose each other and produce an interference pattern. Prove that the resultant intensities at maxima and minima are 4I and zero respectively.

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.Assertion : Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more. Reason (R): Induced emf produced is directly proportional to the magnetic flux.

2.The magnetic field in a plane electromagnetic wave travelling in glass (\( n = 1.5 \)) is given by \[ B_y = (2 \times 10^{-7} \text{ T}) \sin(\alpha x + 1.5 \times 10^{11} t) \] where \( x \) is in metres and \( t \) is in seconds. The value of \( \alpha \) is:

4.Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

5.Nuclides with the same number of neutrons are called:

6.In a Young's double-slit experiment, two waves each of intensity I superpose each other and produce an interference pattern. Prove that the resultant intensities at maxima and minima are 4I and zero respectively.

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Assertion : Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more. Reason (R): Induced emf produced is directly proportional to the magnetic flux.

2.
The magnetic field in a plane electromagnetic wave travelling in glass (\( n = 1.5 \)) is given by \[ B_y = (2 \times 10^{-7} \text{ T}) \sin(\alpha x + 1.5 \times 10^{11} t) \] where \( x \) is in metres and \( t \) is in seconds. The value of \( \alpha \) is:

4.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

5.
Nuclides with the same number of neutrons are called:

6.
In a Young's double-slit experiment, two waves each of intensity I superpose each other and produce an interference pattern. Prove that the resultant intensities at maxima and minima are 4I and zero respectively.