Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 2 / 16D / b

Table of contents
- Solution b

Solution

The temporal component found in part (a) gives directly

E (t) - E (0) = q \int_{0}^{t} E \cdot v (s) d s .

For a constant electric field, this is the work done by the field along the particle trajectory:

E (t) = E (0) + q E \cdot [x (t) - x (0)] .

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