To find the internal resistance of the cell, we can use the formula:

\(V = E - I r\)

Where:
- \( V \) = terminal voltage (2 V)
- \( E \) = electromotive force (emf) of the cell (2.2 V)
- \( I \) = current through the circuit
- \( r \) = internal resistance of the cell

{Step 1: Calculate the Current}

Using Ohm's law, the current (\( I \)) flowing through the resistor is given by:

\(I = \frac{V}{R}\)

Where:
- \( V = 2 \, \text{V} \) (terminal voltage)
- \( R = 4 \, \Omega \)

Thus,

\(I = \frac{2 \, \text{V}}{4 \, \Omega} = 0.5 \, \text{A}\)

{Step 2: Substitute Values into the Formula}

Now substituting \( I \), \( V \), and \( E \) into the formula:

\(2 = 2.2 - 0.5 r\)

{Step 3: Solve for Internal Resistance \( r \)}

Rearranging the equation gives:

\(0.5 r = 2.2 - 2\)
\(0.5 r = 0.2\)
\(r = \frac{0.2}{0.5} = 0.4 \, \Omega\)

Thus, the internal resistance of the cell is:

\(\boxed{0.4 \, \Omega}\)