Continuous Charge Distribution
There are three types of continuous distribution
1. Linear Charge Distribution
2. Surface Charge Distribution
3. Volume Charge Distribution
Linear Charge Distribution
When the charge is distributed uniformly along a line then it is a linear charge distribution.
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| Continuous Charge Distribution |
Linear Charge Density
The ratio of charge dq and dl is called linear charge density. Where dq is charge on extremely small length and dl is very small length.
We denote the linear charge density by `\lamda`
S.I. unit of linear charge density is Coulomb/meter.
Dimension of linear charge density is `[M^0L^{-1}T^1A^1]`
`\lamda = \frac{dq}{dl}`
`dq = \lamda dl`
If the length of the wire is `l` and total charge q is uniformly distributed on the wire, then linear charge density
`\lamda = \frac{q}{l}`
Surface Charge Distribution
When the charge is distributed uniformly along a surface then it is a surface charge distribution.
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| Continuous Charge Distribution |
Surface Charge Density
The ratio of charge dq and dA is called surface charge density. Where dq is a charge on an extremely small area and dA is a very small area.
We denote the surface charge density by `\sigma`
S.I. unit of surface charge density is `\text{Coulomb}/\text{meter}^2`.
Dimension of surface charge density is `[M^0L^{-2}T^1A^1]`
`\lamda = \frac{dq}{dA}`
`dq = \sigma dA`
If the area of the surface is A and total charge q is uniformly distributed on the surface, then surface charge density
`\sigma = \frac{q}{A}`
Volume Charge Distribution
When the charge is distributed uniformly along volume then it is a volume charge distribution.
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| Continuous Charge Distribution |
Volume Charge Density
The ratio of charge dq and dA is called volume charge density. Where dq is a charge on an extremely small area and dA is a very small area.
We denote the volume charge density by `\rho`
S.I. unit of volume charge density is Coulomb/`meter^3`.
Dimension of volume charge density is `[M^0L^{-3}T^1A^1]`
`\rho = \frac{dq}{dV}`
`dq = \rho dV`
If the area of the volume is V and the total charge q is uniformly distributed on volume, then volume charge density.
`\rho = \frac{q}{V}`
MCQs on Continuous Charge Distributions
1. What are the three types of continuous charge distribution?
a) Point, Line, and Surface
b) Linear, Surface, and Volume
c) Positive, Negative, and Neutral
d) Electrostatic, Magnetostatic, and Electromagnetic
Answer: b) Linear, Surface, and Volume
2. Which type of continuous charge distribution is associated with a uniform distribution of charge along a line?
a) Linear Charge Distribution
b) Surface Charge Distribution
c) Volume Charge Distribution
d) Point Charge Distribution
Answer: a) Linear Charge Distribution
3. What is the SI unit of linear charge density?
a) `\text{Coulomb}/\text{meter}^2`
b) Coulomb/meter
c) Coulomb
d) `\text{Coulomb}^2`/meter
Answer: b) Coulomb/meter
4. The ratio of charge dq and dl is called:
a) Surface charge density
b) Volume charge density
c) Linear charge density
d) Electric field intensity
Answer: c) Linear charge density
5. If the length of a wire is 'l' and the total charge 'q' is uniformly distributed on the wire, then the linear charge density is given by:
a) `\rho = q/l`
b) `\sigma = q/l`
c) `\lambda = q/l`
d) `\lambda = l/q`
Answer: c) `\lambda = q/l`
6. Which type of continuous charge distribution is associated with a uniform distribution of charge along a surface?
a) Linear Charge Distribution
b) Surface Charge Distribution
c) Volume Charge Distribution
d) Point Charge Distribution
Answer: b) Surface Charge Distribution
7. What is the SI unit of surface charge density?
a) Coulomb/`\text{meter}^2`
b) Coulomb/meter
c) Coulomb
d) `\text{Coulomb}^2`/meter
Answer: a) Coulomb/`\text{meter}^2`
8. The ratio of charge dq and dA is called:
a) Linear charge density
b) Volume charge density
c) Surface charge density
d) Electric field intensity
Answer: c) Surface charge density
9. If the area of a surface is 'A' and the total charge 'q' is uniformly distributed on the surface, then the surface charge density is given by:
a) `\rho = q/A`
b) `\sigma = q/A`
c) `\lambda = q/A`
d) `\sigma = A/q`
Answer: b) `\sigma = q/A`
10. Which type of continuous charge distribution is associated with a uniform distribution of charge within a volume?
a) Linear Charge Distribution
b) Surface Charge Distribution
c) Volume Charge Distribution
d) Point Charge Distribution
Answer: c) Volume Charge Distribution
Related Question
1. What are the three types of continuous charge distribution?
2. Define linear charge distribution and provide an example.
3. How is linear charge density defined and what are its SI unit and dimensions?
4. What is the relationship between linear charge density and charge distribution on a wire?
5. What is surface charge distribution?
6. Explain the concept of surface charge density and its SI unit and dimensions.
7. How is surface charge density related to the charge distribution on a surface?
8. What is volume charge distribution?
9. Define volume charge density and specify its SI unit and dimensions.
10. How is volume charge density related to the charge distribution within a volume?
Related Numerical Questions
1. A wire of length 2 meters has a total charge of 4 Coulombs uniformly distributed on it. What is the linear charge density?
2. A surface with an area of 0.5 square meters has a total charge of 8 Coulombs uniformly distributed on it. What is the surface charge density?
3. A cube with a volume of 10 cubic meters has a total charge of 20 Coulombs uniformly distributed within it. What is the volume charge density?
4. If the linear charge density on a wire is 0.1 Coulomb/meter and the length of the wire is 5 meters, what is the total charge on the wire?
5. The surface charge density on a circular plate is 2 Coulombs/square meter. If the area of the plate is 3 square meters, what is the total charge on the plate?
6. If the volume charge density within a sphere is 0.05 Coulomb/cubic meter and the volume of the sphere is 8 cubic meters, what is the total charge within the sphere?
7. A wire of length 3 meters has a linear charge density of 0.2 Coulomb/meter. What is the charge on a segment of the wire with a length of 1.5 meters?
8. A surface has a surface charge density of 5 Coulombs/square meter. If the total charge on the surface is 15 Coulombs, what is the area of the surface?
9. The volume charge density within a cube is 0.01 Coulomb/cubic meter. If the volume of the cube is 100 cubic meters, what is the total charge within the cube?
10. If the linear charge density on a wire is 0.05 Coulomb/meter and the total charge on the wire is 1.5 Coulombs, what is the length of the wire?
11. A wire of length 2 meters carries a total charge of 6 Coulombs. Calculate the linear charge density.
12. If a wire has a linear charge density of 10 μC/m, and its length is 5 meters, what is the total charge on the wire?
13. A surface with an area of 0.5 m² has a total charge of 8 μC distributed uniformly. Find the surface charge density.
14. The surface charge density of a charged plate is 2 μC/m². If the area of the plate is 3 m², calculate the total charge on the plate.
15. A sphere has a volume of 1 m³ and a total charge of 12 μC uniformly distributed within it. Determine the volume charge density.
16. If the volume charge density of a charged cube is 5 μC/m³ and its volume is 0.2 m³, what is the total charge inside the cube?
17. A wire has a linear charge density of 8 nC/m and a length of 4 meters. Calculate the charge on a segment of length 1.5 meters.
18. The surface charge density of a charged disk is 3 nC/m². If the disk has a radius of 0.5 meters, what is the charge on a circular region with a radius of 0.2 meters?
19. A sphere has a volume charge density of 2 nC/m³ and a radius of 0.1 meters. Find the charge enclosed within a spherical shell with a radius of 0.05 meters.
20. The volume charge density of a charged cylinder is 4 nC/m³, and its height is 2 meters. Calculate the charge contained in a cylindrical segment with a height of 0.8 meters.
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