A rail gun is a device that consists of two parallel metallic rails of length 0.8 m. At one end, the rails are connected via a power source. A copper wire ($ \rho_{Cu} = 8.96 \, \text{g/cm}^3 $) with a diameter of 0.0011 m makes electrical contact and slides without friction across the rails. The rail gun is placed in a uniform magnetic field of strength 4 T. The magnetic field lines are perpendicular to the plane of the rails. When triggered, the current through the wire is 9000 A.

a. Draw a schematic of this rail gun. Make sure you include all relevant details (like the orientation of the magnetic field with respect to the rails, wire, etc.).

b. What is the acceleration of the wire as it moves across the rails? Express your answer using base SI units.

c. What is the final speed of the wire as it leaves the rails?

In a rail gun, the Lorentz force acts on the current-carrying wire (F = I * L * B), where I is the current, L is the length of the wire in the magnetic field, and B is the magnetic field strength. This force causes the wire to accelerate along the rails. Using Newton's second law (F = m * a), where m is the mass of the wire, we can find the acceleration (a) of the wire.

Given that the density of copper (Pcu) is 8.96 g/cm³ and the diameter of the wire is 0.0011 m, we can find the mass of the wire using the formula for the volume of a cylinder (V = π * r² * h) and multiplying by the density. Then, we convert the mass to kilograms.

With the current (I) given as 9000 A, the length of the wire (L) as 0.8 m, and the magnetic field strength (B) as 4 T, we can calculate the force acting on the wire. Finally, using Newton's second law, we find the acceleration of the wire to be approximately 21766 m/s².

The final speed of the wire as it leaves the rails can be determined using the equations of motion, as the wire experiences uniform acceleration. However, for an accurate calculation, we need to consider factors such as friction and air resistance, which are typically neglected in idealized physics problems. (option c).