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Charge is distributed over the surface of a circle of radius a lying in the xy p

ID: 2128092 • Letter: C

Question

          Charge is distributed over the surface of a circle of radius a lying in the xy plane with origin at the center. The surface density is given in cylindrical coordinates by where A is a constant. What are the units of A? What is the total charge on the circle? Find the force produced by this charge distribution on a point charge located on the z axis.

Can someone tell me if I'm in the right direction? Also, could you help me out solving the integral? Did I make any mistake?

Charge is distributed over the surface of a circle of radius a lying in the xy plane with origin at the center. The surface density is given in cylindrical coordinates by o= Ap^2 where A is a constant. What are the units of A? What is the total charge on the circle? Find the force produced by this charge distribution on a point charge located on the z axis.

Explanation / Answer

Gauss's law for electric field (E):

E?dA = (q in) / (?0)

E = ke q / r2

E = 0 inside a CONDUCTOR

q = ?dA (surface area?)

q = ?dV (volume? )

So...

for r < a, the electric field is not 0 and so

E ? dA = q in / ?0

E (4?r2) = q in / ?0

E = q in / (4?r2?0)

which turns out wrong for r < a. It is still wrong even when I substitute q in as p2. Relevant equations
Gauss's law for electric field (?):

E?dA = (q in) / (?0)

E = ke q / r2

E = 0 inside a CONDUCTOR

q = ?dA (surface area?)

q = ?dV (volume? )

3.

for r < a, the electric field is not 0 and so

E ? dA = q in / ?0

E (4?r2) = q in / ?0

E = q in / (4?r2?0)

which turns out wrong for r < a. It is still wrong even when I substitute q in as pV.


Force = Eq