A singly charged positive ion travels from point to point along a straight line in an…

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A singly charged positive ion travels from point

C

to point

D

along a straight line in an apparatus. The ion’s kinetic energies have been measured at the two points and are listed in the table. Position | Kinetic Energy (J) --------------------------------

C

4.0 \times 10^{-18}

D

1.0 \times 10^{-18}

The electric potential at point

D

+300\,\text{V}

higher than at point

C

. Between the two points the ion experiences a uniform, speed-dependent drag force whose magnitude is proportional to the ion’s speed, producing a total non-conservative energy loss of

1.5 \times 10^{-18}\,\text{J}

along the path. The ion’s mass is

1.2 \times 10^{-26}\,\text{kg}

. No other forces act on the ion. (a) Determine the sign of the ion’s charge. Justify your answer using the information provided. (b) Calculate the ion’s speed at point

C

and at point

D

using the kinetic energies in the table. (c) Using appropriate energy accounting, verify whether the stated non-conservative energy loss of

1.5 \times 10^{-18}\,\text{J}

is consistent with the measured kinetic energies and the given potential difference. Show all steps in your reasoning. (d) Suppose the apparatus is adjusted so that the electric potential difference between

C

and

D

is doubled while all other conditions remain the same, including the drag force law. Predict qualitatively how the ion’s kinetic energy at point

D

would change and justify your prediction.

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