Q. 50

Expert-verifiedFound in: Page 685

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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 .

(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 ,

(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

(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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