# Why does the E-field inside a cylinder =0?

• lodovico
In summary, the problem is asking for the derivation and plotting of the electric field (E) for a long, thin-walled metal tube with a charge per unit length on its surface. The expressions for E are derived for both r > R and r < R, with the results being E = λ/2∏rε0 for r > R and E = 0 for r < R. The reasoning behind the value of 0 for r < R is explained by the fact that the tube is a closed conductor and field lines cannot pass through it. The given values are λ = 2*10^-8 C/m and R = 3cm.
lodovico

## Homework Statement

Figure 24-32 shows a section of a long, thin-walled metal tube of radius R, carrying a charge per unit length  on its surface. Derive expressions for E in terms of distance R from the tube axis, considering both (a) r > R and (b) r < R. Plot your results for the r = 0 to r = 5cm, assuming that  λ= 2*10^-8
C=m//and R = 3cm

[i can't put the figure since the question is in the book]

q = ε0 ∫ E dA

## The Attempt at a Solution

i got the answer to (a) E=λ/2∏rε0

i don't understand why (b) is 0

urgent help due tomorrow

You know that field inside a closed conductor, with no internal charges, is 0. You can think of this as being because field lines cannot pass through it. This tube is 'long'; as long as you are not near the ends, any field reaching in from outside will be small.

## 1. Why does the electric field inside a cylinder equal zero?

The electric field inside a cylinder equals zero because the cylinder acts as a Faraday cage, shielding any external electric fields from penetrating the inside of the cylinder. This is due to the distribution of charges on the surface of the cylinder canceling out any internal electric field.

## 2. Does the electric field inside a cylinder always equal zero?

No, the electric field inside a cylinder will only equal zero if the cylinder is a perfect conductor and there are no external electric fields acting on it. If the cylinder is not a perfect conductor or there are external electric fields present, the electric field inside the cylinder may not equal zero.

## 3. Can the electric field inside a cylinder be changed?

Yes, the electric field inside a cylinder can be changed by altering the charge distribution on the surface of the cylinder or by introducing external electric fields. The electric field inside the cylinder will also change if the cylinder is no longer a perfect conductor.

## 4. How does the radius of a cylinder affect the electric field inside?

The radius of a cylinder does not directly affect the electric field inside, as long as the cylinder is a perfect conductor. However, a larger radius means a larger surface area, which can affect the charge distribution on the surface of the cylinder and therefore alter the electric field inside.

## 5. Why is the electric field inside a cylinder important?

The electric field inside a cylinder is important because it can affect the behavior of electric charges and currents within the cylinder. It is also important in understanding how electric fields interact with conductors and how external electric fields can be shielded or amplified by the geometry of the cylinder.

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