A research team maps the electric potential along the -axis inside a vacuum chamber

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

Problem

A research team maps the electric potential

V

along the

x

-axis inside a vacuum chamber. The potential varies as follows: • At

x=0\,\text{cm}

V=+200\,\text{V}

. • From

x=0\,\text{cm}

x=4\,\text{cm}

V

decreases linearly to

+50\,\text{V}

. • From

x=4\,\text{cm}

x=7\,\text{cm}

V

remains constant at

+50\,\text{V}

. • From

x=7\,\text{cm}

x=10\,\text{cm}

V

increases linearly to

+150\,\text{V}

. A

+1.5\,\mu\text{C}

test charge is moved within this region. (a) Sketch a qualitative graph of

V

versus

x

that reflects the description above. Label numerical values at

x=0,\,4,\,7,

and

10\,\text{cm}

. (b) Describe how the direction and magnitude of the electric field change in each of the three regions where

V

varies (0–4 cm, 4–7 cm, and 7–10 cm). Explain your reasoning without performing numeric calculations. (c) Would positive external work be required, negative external work be required, or would no external work be required to move the test charge slowly from

x=1\,\text{cm}

x=6\,\text{cm}

? Justify your answer in terms of changes in electric potential energy. (d) The same test charge is released from rest at

x=8\,\text{cm}

. Predict qualitatively whether the charge will initially accelerate toward increasing

x

or decreasing

x

, and explain how the electric potential information supports your prediction.

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