3) A cylindrical shell of length 12 m and radius 6 cm carries a uniform surface charge density / (1 nC = ). Find the electric field at (a) r= 2 cm, (b) r = 5.9 cm, (c) r= 6.1 cm, (d) r= 10 cm.

We use a cylindrical Gaussian surface with radius r whose height h is less than 12 m and which shares the same axis with the cylindrical shell. This gives us:

For r<R, so .

For r>R,

a,b) r<6cm, so

c) r>6cm, so d) r>6cm, so

) Four charges are at the corners of a square centered at the origin as follows: q at (-a, +a); 2q at (a, a); -3q at (a, -a); and 6q at (-a, -a). Find (a) the electric field at the origin and (b) the potential at the origin.

a)

Let

Let

b)