- (40 points) A 1.0 m section of an aluminum wire with 2.0 mm diameter carries 1.0 Ampere of electric current in a circuit and has an DC electrical resistance of 0.00845 Ω. The wire is along the x-axis, y=0 and z=0.

- What is the number of aluminum atoms in 1.0 m of this wire?
- What is the electrical conductivity of this Aluminum wire?
- Calculate the number of conduction electrons in this 1.0 m of wire.
- Calculate the potential difference across this 1.0 m aluminum wire.
- Calculate the power dissipation on this 1.0 m wire.
- Calculate the electric current density vector, J, in this wire.
- Calculate the average electric field in this wire.
- Calculate the Al
^{+3}atom density in this wire. - What is the “+” charge density?
- Calculate the conduction electron density in this wire.
- What is the net electric charge density on this wire?
- Calculate the average speed of electrons in this wire.
- A test charge electron coming out of a 1000 V electron gun is travelling along x-axis at y= 0.20 m, z= 0. What is the speed of this electron if the process taking place in vacuum?
- What is the velocity vector, v, of this test electron at that moment where travelling along x-axis?
- What is the “+” charge density observed from the inertial frame of moving along x-axis with the same speed as test electron?
- What is the speed of conduction electrons in wire observed from the inertial frame of moving along x-axis with the same speed as test electron?
- What is the “-” conduction electron charge density observed from the inertial frame of moving along x-axis with the same speed as test electron?
- What is the net charge density observed from the inertial frame of moving along x-axis with the same speed as test electron?
- What is the force vector on this test electron at that moment?

- (30) points) A small 1.0 mm water droplet charged with a charge of 2.0×10
^{-6}Coulomb is hanging (x=0, y=0, z=5 cm) over a very large electrically charged metal plane placed on xy plane at z=0.

- What is the electrical surface charge density of this metal plate?
- What is the electrical potential value at the point of this charge?
- Determine the electric field vector function at z>0 space ( exclude inside the droplet)

- (30 points) A vector function given as : E = (2xy
^{2}+ z^{3}, 2x^{2}y, 3xz^{2}) with a constant to adjust units.

- Is this a valid function representing static electric field? Show it why or why not ?
- Find charge density function ?
- Find the associated potential function φ(x, y, z).