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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

A very long, uniformly charged cylinder has radius and linear charge density. Find the cylinder's electric field strength (a) outside the cylinder, , and (b) inside the cylinder, . (c) Show that your answers to parts a and b match at the boundary,

a.Electric field strength outside the cylinder is .

b.Electric field strength inside the cylinder is .

c.The answers match at the boundary at .

See the step by step solution

Step by Step Solution

Step 1: Calculation for electric field outside the cylinder (part a)

(a).

Electric flux,

For charge,

The cylinder has linear charge densityand length.

the charge surrounded by

The flux through the top and bottom faces of the cylinder is zero since they are perpendicular to the electric field.

The flux through the cylinder's wall, on the other hand, is the highest.

So,

For ,

Step 2: Calculation of electric field inside the cylinder (part b)

(b).

The cylinder's volume charge density is equal to the cylinder's charge divided by its volume.

The electric field inside the cylinder is formed by

For a point at distance ,

The charge density is ,

Where is the linear charge density.

As a result, given a point inside the cylinder, the electric field is

Step 3: match at the boundary (part c)

(c).

The radius of the gaussian surfaceand the radius of the cylinderare the same.

In component (b), the electric field will be

Because this is the same electric field as in part (a), our responses are identical at the border.

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