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An electrical conductor XY carries a current I as shown - Edexcel - A-Level Physics - Question 12 - 2023 - Paper 1
Question 12
An electrical conductor XY carries a current I as shown. The current density j is defined as j = \frac{I}{A} where A is the cross-sectional area of the conductor. ... show full transcript
Worked Solution & Example Answer:An electrical conductor XY carries a current I as shown - Edexcel - A-Level Physics - Question 12 - 2023 - Paper 1
Step 1
State what is meant by a vector quantity.
Answer
A vector quantity has both magnitude and direction. This means that a vector is not defined solely by its size, but also by the direction in which it points. For example, current density is a vector quantity because it describes how much current flows per unit area in a specific direction.
Step 2
Explain this affects the drift velocity of the free electrons in the conductor.
Answer
When the current I remains constant but the cross-sectional area A decreases towards end Y of the conductor, the current density j increases, according to the equation:
Since j is directly proportional to the drift velocity v_d, we can express this relationship as:
where n is the number density of charge carriers and e is the charge of an electron. As A decreases,
- The quantity v_d must increase to ensure that the product results in a higher j, matching the constant current I flowing through the conductor. Thus, as area decreases, drift velocity increases so that the same amount of current can still be conducted through a smaller cross-section.