A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of `lambda`, and the cylinder has a net charge per unit length of `2lambda`. From this information, use Gauss's law to find (i) the charge per unit length on the inner and outer surfaces of the cylinder and (ii) the electric field outside the cylinder, a distance r from the axis.

Explanation

To solve the problem step by step, we will use Gauss's law to find the charge per unit length on the inner and outer surfaces of the hollow metal cylinder and the electric field outside the cylinder.

### Step 1: Understanding the Setup
We have a long straight wire with a charge per unit length of \( \lambda \) and a hollow metal cylinder with a net charge per unit length of \( 2\lambda \). The wire is placed along the axis of the cylinder.

### Step 2: Charge Distribution on the Cylinder
1. **Inner Surface Charge**:
- The electric field inside a conductor in electrostatic equilibrium is zero. Therefore, the charge on the inner surface of the cylinder must be such that it cancels the electric field due to the wire.
...