Current Electricity
NCERT Class 12 Physics - Chapter 3 | High-Yield Concepts & Advanced Problems
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Question 1
A steady direct current flows through a metallic wire whose cross-sectional area increases monotonically from the left end to the right end. Which of the following macroscopic quantities remains strictly constant along the length of this non-uniform wire?
Concept Involved: Conservation of charge in steady-state current systems (NCERT Section 3.4).
Explanation: Under steady-state conditions, charge cannot accumulate at any segment of an isolated conductor. Therefore, the total number of charges entering any cross-section per unit time must equal the number of charges leaving it. This makes the total electric current (I) completely constant along the entire length of the wire. However, current density is defined as J = I / A. Since the area (A) increases from left to right, J must decrease. Furthermore, because J = σE, the internal electric field (E) must also decrease. Finally, since drift velocity is given by v_d = I / (nAe), it varies inversely with the area and will decrease along the wire. Thus, only the total electric current remains constant.
Common Misconception: Students often assume that because Ohm's law applies locally, the electric field or current density
Explanation: Under steady-state conditions, charge cannot accumulate at any segment of an isolated conductor. Therefore, the total number of charges entering any cross-section per unit time must equal the number of charges leaving it. This makes the total electric current (I) completely constant along the entire length of the wire. However, current density is defined as J = I / A. Since the area (A) increases from left to right, J must decrease. Furthermore, because J = σE, the internal electric field (E) must also decrease. Finally, since drift velocity is given by v_d = I / (nAe), it varies inversely with the area and will decrease along the wire. Thus, only the total electric current remains constant.
Common Misconception: Students often assume that because Ohm's law applies locally, the electric field or current density
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