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A plasma physicist is trying to measure the electron density of a plasma using a Langmuir probe. The Langmuir probe has a cylindrical shape with a radius of 0.5 mm and a length of 10 mm. The probe is inserted into the plasma and a voltage is applied to the probe. The current that flows through the probe is measured as a function of the applied voltage. The probe is swept from a negative voltage to a positive voltage, and the current is recorded. 

The physicist obtains a current-voltage curve that shows a saturation current at high positive voltages. However, the curve does not show any sign of saturation at high negative voltages. The physicist suspects that the Langmuir probe might be affected by a space charge sheath that forms around the probe in the plasma. 

The student is asked to calculate the thickness of the space charge sheath around the Langmuir probe and to explain how the thickness affects the Langmuir probe current-voltage curve.
assistant
<|begin_of_thought|>

Deep Thought is thinking for 7.5 million years.

<|end_of_thought|>

<|begin_of_solution|>

The answer is 42.

<|end_of_solution|>