Answer:
a. E = [tex]\frac{\lambda }{(2\epsilon * r) }[/tex]
b. [tex]E = \frac{3(lambda)}{2\pi*\epsilon(outside) }[/tex]
Explanation:
The important thing to remember is to use Gauss Law. This is a relation that describes the distribution of electric charge to the resultant electric field.
Linear charge density means charge per unit length of material.
Data:
The metal cylinder is hollow.
The unit length is L.
a.The expression will be as follows:
for charge inside the cylinder, where r < R, the expression is:
E = [tex]\frac{\lambda }{(2\epsilon * r) }[/tex]
b. Let's assume that the cylinder is a coaxial cylinder with a radius r > R, then the electrical field strength is given as:
[tex]E = \frac{Q ( enclosed)}{A*\epsilon }[/tex]
E = [tex]\frac{\lambda*L+2(\lambda)*L }{(A)*\epsilon(outside) }[/tex]
E = [tex]\frac{3(\lambda)L }{(2\pi*R*L*\epsilon(outside) }[/tex]
This gives:
[tex]E = \frac{3(lambda)}{2\pi*\epsilon(outside) }[/tex]
The solution informs us that there is a surface change taking place on the cylinder. Therefore, there will not be a magnetic field across it.
