# Gauss' Law: Charge enclosed zero = E field zero?

## Homework Statement

A cylindrical shell of radius R and length H has its charge uniformly distributed on its curved surface

Find the electric field at a point P from the axis, a distance r away, measured radially outward from the midpoint of the shell such that R>r

## Homework Equations

φ = ∫E⋅dA = Qenc / ∈o

## The Attempt at a Solution

I constructed a gaussian surface (cylinder) inside the larger cylinder of radius R.

I realize, my chosen gaussian surface encloses no charge ∴ φ & Qenc are both zero.

I have been told I am not allowed to simply jump and say the E field must also then be zero if the flux is zero, but for this case, since the charge on the outer cylinder is uniformly distributed, does that also mean the net electric field at point P must be zero?

If not, please shed some light on this!

Thank you

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SammyS
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## Homework Statement

A cylindrical shell of radius R and length H has its charge uniformly distributed on its curved surface

Find the electric field at a point P from the axis, a distance r away, measured radially outward from the midpoint of the shell such that R>r

## Homework Equations

φ = ∫E⋅dA = Qenc / ∈o

## The Attempt at a Solution

I constructed a gaussian surface (cylinder) inside the larger cylinder of radius R.

I realize, my chosen gaussian surface encloses no charge ∴ φ & Qenc are both zero.

I have been told I am not allowed to simply jump and say the E field must also then be zero if the flux is zero, but for this case, since the charge on the outer cylinder is uniformly distributed, does that also mean the net electric field at point P must be zero?

If not, please shed some light on this!

Thank you
Is there sufficient symmetry to conclude that the field is zero everywhere inside to charge distribution?

Is there sufficient symmetry to conclude that the field is zero everywhere inside to charge distribution?
Yes.

I think that answers my question, so then, we should be examining at the symmetry of the chosen surface with respect to the original surface.

SammyS
Staff Emeritus