Why is a cylindrical Gaussian surface used in determining the field of a uniform line charge?

A cylindrical Gaussian surface is used when finding the electric field or the flux produced by any of the following: an infinitely long line of uniform charge. an infinite plane of uniform charge. an infinitely long cylinder of uniform charge.

Why do we choose a Gaussian surface?

We now need to choose a gaussian surface that will make the flux integral easy to evaluate. Ideally, we can find a surface over which the electric field makes the same angle with the surface and over which the electric field is constant in magnitude.

Why is a spherical Gaussian surface appropriate when calculating the electric field of a point charge?

Considering a Gaussian surface in the form of a sphere at radius r, the electric field has the same magnitude at every point of the sphere and is directed outward. The electric flux is then just the electric field times the area of the sphere. so this is seen to be consistent with Coulomb’s law.

In which direction is the electric field on the cylindrical Gaussian surface?

outward
The electric field of an infinite cylindrical conductor with a uniform linear charge density can be obtained by using Gauss’ law. Considering a Gaussian surface in the form of a cylinder at radius r > R, the electric field has the same magnitude at every point of the cylinder and is directed outward.

Why can a Gaussian surface not pass?

The Gaussian surface doesn’t pass through any discrete charge. This is because electric field due to a system of discrete charges is not well defined at the location of any charge. However, the Gaussian surface can pass through a continuous charge distribution.

What is the use of Gaussian surface also mention the importance of Gauss theorem?

(1) Gauss’s law is very useful in calculating the electric field in case of problems where it is possible to construct a closed surface. Such surface is called Gaussian surface. (2) Gauss’s law is true for any closed surface, no matter what its shape or size.

What is the use of Gaussian surface also mention the importance of Gaussian theorem?

What are the properties of Gaussian surface?

What is Gaussian Pillbox? The Gaussian pillbox is the surface with an infinite charge of uniform charge density is used to determine the electric field.

How do you choose a Gaussian surface?

How to determine a Gaussian surface?

1. Step 1: Select the surface from a body or object.
2. Step 2: Check direction of electric field (E)
3. Step 3: Check the area vector (A)
4. Step 4: Check the angle between area vector (A) and electric field (E)

What is the outward electric flux through the cylinder?

Thus, flux through the side of the cylinder is 0. (c) Net outward flux through side of the cylinder: This flux is due to the surface 1 and 2. Thus, the net outward flux through side of the cylinder is 3.14 $N{m^2}{C^{ – 1}}$.

Is the electric field outside the cylinder the same as if all the charge were on the axis?

Since the electric field must be constant everywhere on the tube wall, the electric field must be zero. Note that the result is the same as if the charge were concentrated in a line along the axis.

What is the nature of Gaussian surface?

A Gaussian surface is an imaginary closed surface around a charge in a 3 dimensional space. The total amount of flux is calculated by using this surface. Now, the Gaussian surface is an imaginary surface. So it can never be electrical and magnetic in nature.

Is the electric field inside a cylindridal Gaussian surface?

The electric field inside an infinite cylinder of uniform charge is radially outward (by symmetry), but a cylindridal Gaussian surface would enclose less than the total charge Q. Note that the limit at r= R agrees with the expression for r >= R.

What is the electric flux of a Gaussian cylinder?

Considering a Gaussian surfacein the form of a cylinder at radius r > R, the electric field has the same magnitude at every point of the cylinder and is directed outward. The electric flux is then just the electric field times the area of the cylinder.

What is the electric field inside an infinite cylinder of uniform?

The electric field inside an infinite cylinder of uniform charge is radially outward (by symmetry), but a cylindridal Gaussian surface would enclose less than the total charge Q. The charge inside a radius r is given by the ratio of the volumes:

What is Gaussian surface in case of cylindrical symmetry?

The Gaussian surface in the case of cylindrical symmetry. The electric field at a patch is either parallel or perpendicular to the normal to the patch of the Gaussian surface. The electric field is perpendicular to the cylindrical side and parallel to the planar end caps of the surface. The flux through the cylindrical part is