A solid cylindrical conductor of radius 2.0 mm carries mobile electrons of number density

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

n=8.0\times10^{28}\,\text{m}^{-3}

. In a laboratory demonstration the conductor is prepared so that, at an instant of time, electrons in the inner core of radius 1.0 mm drift to the right with speed

v_{1}=1.5\times10^{-3}\,\text{m}\,\text{s}^{-1}

, while electrons in the outer cylindrical shell drift to the left with speed

v_{2}

. (a) Derive an expression for the net conventional current

I

through a cross-section of the wire in terms of

v_{1}

v_{2}

n

, the elementary charge

e

, and the specified radii. (b) Determine the value of

v_{2}

required so that the net current is zero. (c) Calculate the magnitude of the electric charge that crosses the mid-plane of the wire in a time interval of 2.0 ms for the inner core alone. (d) Despite your answer in part (b), explain why significant magnetic effects would still be produced in the space between the two cylindrical regions.

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