Finding an electric field at a point from a line of charge

In summary, the question asks for the electric field at point p, 6cm from the central axis, for a thin insulating rod with charge density lambda=+5nC/m arranged inside a thin conducting cylindrical shell of radius r =3 cm. Using Gauss's law, the solution is found by taking the area of the Gaussian cylindrical surface at 6 cm radius and multiplying it by the electrical intensity. The answer is half of the calculated value due to the presence of the conducting shell.
  • #1
Physiqs
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Homework Statement



A thin insulating rod with charge density lambda=+5nC/m is arranged inside a thin conducting cylindrical shell of radius r =3 cm. The rod and the shell are on the same axis, and infinite in length.
What is electric field at point p? 6cm from the central axis.

exam7.jpg


Homework Equations


Gauss's law : E*dA = Qenc/epsilon

The Attempt at a Solution


The question before this was actually to find the sigma.. which was 26.526nC/m^2. So I used sigma in the gauss's law. E*dA( area of cylindrical wall) = (sigma*A)/epsilon and got 2998. However, the answer was exactly the half of that(1499) ... Why?
 
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  • #2
Just revise the content on field near a non conducting sheet and a conducting sheet. A factor of 2 comes there as there is no field on one side of a conducting sheet as field inside conductor has to be zero. Also i think the answer should be same that you would get in the absence of the infinite cylindrical shell.
 
  • #3
Physiqs said:

Homework Statement



A thin insulating rod with charge density lambda=+5nC/m is arranged inside a thin conducting cylindrical shell of radius r =3 cm. The rod and the shell are on the same axis, and infinite in length.
What is electric field at point p? 6cm from the central axis.

exam7.jpg


Homework Equations


Gauss's law : E*dA = Qenc/epsilon

The Attempt at a Solution


The question before this was actually to find the sigma.. which was 26.526nC/m^2. So I used sigma in the gauss's law. E*dA( area of cylindrical wall) = (sigma*A)/epsilon and got 2998. However, the answer was exactly the half of that(1499) ... Why?

i think you are making an error in calculation...
the line of charge has given charge per unit length. and the Gaussian cylindrical surface (hypothetical) to calculate the flux through it is to be constructed at 6 cm radius so take the area of this surface times the electrical intensity and apply Gauss theorem.
 
  • #4
very close to a non-conducting sheet of charge E = σ/ε₀ and for a conducting sheet of charge E' = σ/(2ε₀)
 
  • #5
Last post was not correct. It may be read as:

very close to a non-conducting sheet of charge E = σ/(2ε₀) and for a conducting sheet of charge E' = σ/ε₀
 

1. What is the formula for finding the electric field at a point from a line of charge?

The formula for finding the electric field at a point from a line of charge is E = kλ/r, where E is the electric field, k is the Coulomb's constant, λ is the linear charge density of the line, and r is the distance from the point to the line.

2. How do you determine the direction of the electric field at a point from a line of charge?

The direction of the electric field at a point from a line of charge is determined by the right-hand rule. If you point your thumb in the direction of the line of charge, the curl of your fingers will indicate the direction of the electric field.

3. Can the electric field at a point from a line of charge ever be zero?

Yes, the electric field at a point from a line of charge can be zero if the point is located at the midpoint of the line of charge, or if the line of charge is infinitely long and the point is at an infinite distance from the line.

4. How does the electric field at a point from a line of charge change as the distance from the line increases?

The electric field at a point from a line of charge decreases as the distance from the line increases. This is because the electric field follows an inverse square law, meaning that it decreases proportionally to the square of the distance.

5. Can the electric field at a point from a line of charge ever be negative?

Yes, the electric field at a point from a line of charge can be negative if the point is located on the opposite side of the line from the direction of the electric field. This indicates that the electric field is directed in the opposite direction from the line of charge.

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